But Rand knows his mistrust is not really based on anything other than what at the time he believed to be his insanity. Going by hard facts (beware the opposite of the PoV trap - thinking the characters know or perceive things the way the readers do), Rand has no real reason to be more suspicious of Taim than other people. He just doesn't have the time to check up on every little quirk among all his minions. Taim has thoroughly done his job regarding the building of the Black Tower. Blaming him for the renegades, if you have not have not read their PoVs to know about his orders to them concerning their
assassination attempt, is like blaming Egwene for the transgressions of the Salidar embassy. Bashere noted their disenchantment over the course of the Altara campaign, and Logain's own faction, who are reflexively suspicious of anyone associated with Taim, also first think that's the motivation for the desertion. Taim's excuse to Rand is plausible to both perspicacious outsiders and to those familiar with (and suspicious of) Taim. Rand's question to Logain is on point - why would a Darkfriend do all that Taim has done. Note that Rand's entourage (aside from Narishma and Dashiva) is chosen from guys who came to him first, and were not found by Taim - he almost certainly choose them for that reason. If there was anything untoward about how Taim runs things, he'd have found out from them. Even at his worst, no one accuses Taim of openly running a Dark Tower - his purported Darkfriend cell is among his clique and their secret lessons. But there are justifications for that too. The charge of favoritism could be credibly laid at the feet of Elaida, Egwene and Siuan as well. They have had their secret inner circles, restricted advanced knowledge and skills to certain trusted individuals and even met with a select group of their most advanced followers behind closed doors. The arrogance of his pets might be an indicator of universal low character...or it might be an all too understandable trait of guys who were anonymous civilians a year ago and are now literally the deadliest and most powerful men in the world. Arrogance is the hallmark of wetlander channelers, and hardly something that can be pinned entirely on Mazrim Taim.

As far as Logain goes, we have exactly zero indication of his good character, aside from the occasional flash of warrior cameraderie, which, take it from me, can pop up in even the biggest jerks who make their living bearing weapons in a uniform. Being a good soldier is in no way proof of good character (i.e. Hitler), and aside from that, Rand has seen precious little in the way of good from a man who is not only the sole source regarding Taim's villainy, but who stands to profit the most from Taim's downfall. For that matter, even we the readers have seen very little goodness from Logain, and zero evidence of any loyalty to Rand that is not forced, even setting aside quotes like "Whatever the Lord Dragon ordered, I trust I've made my orders clear." For most of the time we have seen Logain, he was either being an arrogant douche, or else a whimpering, whining emo type. He came to the Black Tower in a time when he had no other choices, was welcomed in a fashion that made most observers believe he and Taim were friends, and apparently started right away building up his own personality cult in opposition to the M'Hael. Now he comes to Rand with a wild conspiracy theory about the guy who has built up Rand's most powerful asset being a darkfriend. The idea that a darkfriend would work so assiduously to benefit the Dragon Reborn because the Shadow wants him to be powerful for abstract and intangible reasons is a bit hard to swallow for someone who has not been reading several books with Moridin's PoV and dialogue. We can only credit Logain because our faith in the good guys' eventual victory means that Min's viewing points to Logain being on the good side. For all Rand knows, that glory is going to come from betraying him and or even usurping the credit for his victory. Taim himself suggested a path to glory as Rand's right-hand man, so who is to say it wouldn't work for Logain...if he could just displace that pesky Taim, who stands between him and public command of the Tower.

The next sign that "Rand's ally" is a positive indicator in the mind of the rebel Aes Sedai will be the first. Mat's appearance in Salidar aroused fear and panic. Rand's authority over the Asha'man never came up in the debate about bringing them into circles for defense. Aes Sedai grumble about how much trouble Rand's appointment of stewards will cause. Why don't you show me ONE place in the series where ANY Aes Sedai took being Rand's ally for a good mark on someone's score card.
Not to mention, just about the worst way to promote cooperation between Asha'man and Aes Sedai and avoid a fight between them is to say something like "You can bond Asha'man as Warders if you like, just as long as you can pry them away from their evil tyrant leader!"

And that, of couse, is even assuming Rand has any real reason to believe that of Taim. Find some evidence of which Rand would be aware, or some way he could obtain that information? Hanging around the Black Tower more means leaving all the other business of the world in the lurch and will only show him what Taim wants him to see. Using Asha'man as informants presumes he can trust these men he has known less time than Taim.

All you have is her own assertions that her motives are better. Where the hell does an 18 year old with no experience of the world outside the White Tower, a farming village and an Aiel camp get off deciding what all that entails? In practice, her actions are identical to self-serving power-seeking politics. All that seperates her from a self-serving, power-seeking politician and tyrant is paving material for the road to hell.

In any event, a woman whose Keeper of the Chronicles was a Darkfriend, as well as her masseuse and personal confidant, has no business castigating Rand for allowing a Darkfriend into a position of power and trust, especially as Taim has been both a greater help and more competant than Sheriam on her best day.