In the case of Stannis, you are assuming that is not a deliberate omission. Tyrion addresses the issue of how he figured it out back in CoK, with Varys giving enough of an answer for him to drop the subject, suggesting someone might have told Stannis in an effort to cause trouble. That's all Tyrion needs, because for all practical purposes, dealing with Stannis' knowledge is more important than how he came by it. Maybe you think it is sloppy writing or something to put in Varys & Baelish as plot movers, but I don't see how that's evidence of a change of plan or anything, when they were all but introduced in that role, as manipulators each playing his own game against Robert's reign.
As far as Catelyn's blindness to the possibility of a frame-up, it's the trust thing. The whole point of honor in a society without a higher authority is that you are able to count on people to always be reliable on certain issues, in order to enable said society to function. That's why it is most associated with barbarians, who have no government to answer to, or aristocrats, who sit atop the social structure, and also answer to no one. Peasants don't need honor, because the nobles keep them in line. A peasant cheats another one, the victim complains to a noble. A noble cheats another noble, and he can complain to their liege lord or king, but making the perp answer for it can be tricky, since he lives in a fort, and has troops. So they have this code of honor, that, like diplomatic customs, and international law, hinges on reciprocity. Catelyn and Ned can see the consequences of breaking with the code, which is the loss of all trust and reliability. Petyr has very little to gain by sticking to it, since he'll never have the credibility others with a family reputation to augment their own do, and believes himself smart enough to evade the consequences of breaking it. That's why he advises Sansa to always make sure "you have clean hands." Since it would be suicidal for a guy with no apparent resources to break faith with the most powerful family he has ever had access to, Catelyn assumes he is playing her straight. She also assumes her sister is doing the same thing, because the Tullys are raised to keep the faith with one another, and be there for each other - "Family, Duty, Honor." The notion of protecting your own, no matter what, is a society-wide meme, at least among the older and more powerful noble Houses. The Tullys have their motto, the Lannister go to war over even their least valuable family members, the Starks use wolf-pack imagery, but it all boils down to an effective survival tactic. The families with that mentality tend to survive over ones that go their own way. And sure enough, Lysa dies, alone and all but isolated, having failed to stick up for her family throughout the books. Catelyn's betrayal and fall came out in other ways, but not out of breaking the code. Her last action is to follow through with her threatened reciprocity when her son is murdered. While it didn't do her much good, in other circumstances, people might have recalled that even in her despair, she slaughtered an inoffensive and harmless hostage in retaliation for her son's death, and decided to be a little more cautious when fucking with a Tully.
The point of that digression, which kind of ran away from me, is that Catelyn acts in a sensible manner for the time and place in which she lives, and sort of expects other people to do the same thing. You keep faith with your high-born patrons, or no powerful nobles will trust you ever again. Only Catelyn and Ned know how it was Petyr who set them on that course, and had they survived his machinations, it would have blown up in his face, and badly. A comparison would be a like a rational man with a gun pointed at an unarmed man. He would be presumed to have the advantage, unless the other guy either has a secret advantage or is a suicidal zealot who does not value survival the way the rational guy does. In the former case, the "unarmed" man might risk his adversary shooting, because he has a chance to survive and win. Likewise, Petyr is counting on things Catelyn is not aware of to enable him to survive his deception of his one-time benefactor family. Also, she doesn't know about his and Lysa's affair and aborted child, so that's an irrational factor. Without the knowledge of his reasons for resenting her and her family (and the Starks in the bargain), she lacks a reason to assume malice on his part.
As far as the stand-alone plausibility of the actual assassination, AND Tyrion's involvement, there is no reason, but that's what Catelyn wants to find out. So far as she knows, there is no reason for them to have murdered her brother-in-law. By the time she meets up with Tyrion, there have been other things she will have heard about, like Cersei's malice in the wolf incident, and her excessive influence at court. And she has a message from her sister, that Lysa took great pains to deliver in secret, highlighting its importance, which indicts the family of hostility towards her own. Jon Arryn might just be some guy who happened to be married to a sister she hasn't seen in years, but that's not important. To the Tully code, he's still family, thus his enemies are her enemies, and her children's and husband's enemies by extension (again, assuming reciprocity from Lysa et al, this is not a weakness, either). She is unaware of Lysa's deterioration or inconstancy, nor can she conceive of a reason why her sister would mislead her.
While Petyr's frame-job looks thin to a modern, individualistic mentality, to a familist mentality, where trust and reputation count for more than rational objective analysis (purely rational, purely objective analysis being more of a idealized notion than a practical reality most of the time anyway, as well as failing to take into account human irrationality), his story is previously confirmed. She is not dealing with sketchy rumors, from her perspective, she is dealing with two unimpeachable sources independently confirming her suspicions.
The actual sequence of the assassination attempt is not rational in the sense of everyone doing the absolute best and smartest thing, but the contemporary habit of referring to irrational choices as plot holes is as absurd & unrealistic as assuming rational objectivity is possible in every analysis. Yes, Joffrey's decision was senseless, petty and vicious, but what, exactly in Joffrey's prior and subsequent history is NOT? His sadism and homicidal inclinations are a consistent character trait, and an excuse to cause someone's death is exactly the sort of thing he'd leap at, not realizing how relatively soon he'd get many more such opportunities. He's grown up at court, watching intrigue and plots since his birth, so the chance to order a stealthy assassination is something he would plausibly leap at. The sloppiness and clumsiness of the attempt are actually more realistic than a better-executed plot would have been from someone with his age and solipsistic limitations.
No, it's actually very plausible and rational behavior. The possibility of them believing him is very slim. Almost no one believes in the Others, absent childlike acceptance of stories, mystic knowledge, or religious fanaticism, until they encounter them or their minions. If anyone would be familiar with what the black brothers were likely to believe, it would be a veteran like Gared. On the other hand, he is more likely to be thought a coward who bailed on two companions. The brothers might be theoretical equals, but Waymar Royce is nobleborn, and as a practical matter, you'd get in a lot of trouble if you left him to die. He's the one Mormont sends Ben Stark out to look for, after all.
But even if they DID believe Gared, so what? From his point of view, what happens then? A parade, a medal, hot chicks falling all over him? No, Jeor Mormont and Benjen Stark order him to mount up and lead them to the last place he saw the Others and the wights, to guide a force in strength back to the scene of the most horrible thing he has ever encountered in his life. Why in the living fuck would you go back to that, or take any course of action leading to it? Sure, from the perspective of a fantasy reader looking to read about a battle between humans and monsters, that's the desirable outcome, but it flies directly in the face of what any normal human being would WANT to do. From the point of view of personal survival, bringing a warning back to the Night's Watch is the idiotic, plot-driven behavior.
Sure, he'd be more comfortable, with no one seeking to kill him for desertion at Castle Black, but like, 90% of the men of the Watch are there because they chose a lower level of survival and a less desirable life, over certain death. Living in perpetual winter, next to the world's biggest chunk of ice, with a chance of getting killed by wildings down the road, is not a remotely pleasant prospect, but it's better than getting hanged tomorrow. Likewise, getting hunted across the continent as a deserter, marked for summary execution is not a great future prospect, but it's still better than being among the first wave of the Other's victims, or whatever he witnessed happen to Royce & Wil.
R+L=J. If you know what that means, then roll over for the theory: There are no actual spoilers, and nothing in it is confirmed by outside sources so far as I know, but enough people believe this one (formulated independently by many readers), that it is considered the next thing to canon.
The Theory is that Rhaegar & Lyanna were having a tryst, not an abduction-rape. He was inspired by the prophecy of the Prince who is promised, and believed that his son Aegon needed another sibling to fulfil the prophecy, so his child by Lyanna would be all important, which is why he had the three best Kingsguard with her and their baby. The rationale for why they would fight Ned at all is kind of suspect, but even before I hypothesized the R+L=J thing, my assumption was that they were kind of committing suicide by cop. That was the point of the conversation with Ned. He was offering them a way to survive - they could go into exile, with or without Viserys & his mom/sister like Ser Willem Darry, or bend the knee and serve in Robert's Kingsguard like Ser Barristan. Instead, they decided to go out with honor. Maybe it was also because they would be honor bound to share the secret of Rhaegar's child with their new liege, and like Ned, feared he'd kill Lyanna's baby like he accepted Tywin's murder of Elia's. I would guess that Ned only took six guys because they were among his closest friends (they included Howland Reed, presumably the little crannogman of Meera's tale, who was saved & protected by Lyanna & her brothers; Brandon's squire; a member of House Cassel, who apparently serve the Starks very closely, given that his brother is the master-at-arms & castellan at Winterfell, and son would be captain of the guard; and the husband and the kinsman of Brandon's ex-girlfriend) and the ones he most trusted with something like his sister's honor. He was, depending on what he knew at the time, either coming to rescue his sister from a captivity in which she had been raped, or to break the news of her lover's death (not to mention that of their fathr & big brother), and take her home. Her condition or reaction in either scenario would not be the kind of thing you want half the peasants in the North gossiping about. Their remaining so long at the tower is explained by the assumption that Lyanna was pregnant (also explaining why Rhaegar only joined the war at the last minute, when it was his actions that kicked it off), she gave birth only very shortly before Ned's arrival, and presumably died of complications or weakness from the birthing.
End Theory
Depending on the general public consensus on what passed between Rhaegar & Lyanna, they would probably be assuming that she was being kept in a love nest or something. They also probably assume Ned is either telling the truth in whatever version of events he gave out (since Cersei knows he was responsible for the death of Arthur Dayne, I'd guess he stuck close to the truth), or at worst, glossing over things that might be embarassing to the family. Since nothing has come of it in 14 years, and Ned isn't much involved in the general run of events, there really isn't any reason to speculate. The rest of the realm probably views them as boring hicks from a backwater region.
“Tolerance is the virtue of the man without convictions.” GK Chesteron
Inde muagdhe Aes Sedai misain ye!
Deus Vult!
*MySmiley*