The logic is simple:

1) There are wards that detect male channelers
2) There are wards that signal the channeler who set them up an alert if someone enters or passes a certain point
3) There are wards and weaves that enable female channelers detect male channelers
4) Graendal's palace may have are defenses she never listed, but we do know that it is surrounded with various weaves that provide for her comfort, such as the temperature augmenting weave - we even see her use a variant earlier in the book
Thus, I actually think you need to suspect rationality in order to believe that she doesn't have defenses around herself besides creature comforts.

So in my opinion, it may be a combination of factors that lead to her being alerted. The most obvious factor may simply be that she did not get orders to meet with or confront the Dragon and she knows of multiple Chosen punished for not obeying orders. It is the most obvious because her goal is not to turn Rand, capture him, or defeat him - her goal is mouch more straightforward: follow Moridin's commands as he is Nae'blis and then choose the right moment to defeat Moridin so she could claim the title.

Here is my problem with your reasoning:
1) Graendal was at the Cleansing, and saw the vast amounts of the Power being generated and felt the amounts of saidar - she had no reason to doubt that the male Access Key was destroyed; given what she witnessed, it would be uncharacteristic for her not to assume he had it on him. Especially since Rand took to wearing it on his belt, riding saddle and even had his clothing revised to keep it on him
2) The last time Rand dropped in to a Forsaken's palace (Rahvin's) it didn't turn out too well. I think it is flawed reasoning to assume she would hold her ground when she had other headquarters set up for just such an occurrence
3) She said she had two overall tactics in regards to Rand - throw herself at his mercy or run away. I think it is flawed reasoning to discount this statement and think that she would now violate direct orders to meet with him when she is very close to her goal
4) Her M.O. (once again) - she doesn't like it when she has to meet on other people's territory but she especially doesn't like it when they come unannounced to hers. The entire section is rather vapid - Rand sends a nobleman running through the forest to her palace and then the same nobleman heads back, where he is taken by Aiel and lead back to Rand. There is a lot of potential for her to simply escape and leave a dupe at the palace for Rand to meet. It is a little ridiculous to assume that since she knows Rand can channel, she wouldn't find it alarming to have a messenger arrive suddenly and totally discount the idea that Rand was trying to keep her there to trap her.
5) Your reasoning is flawed in terms of the messengers: Graendal has Arad Doman well in hand, and is very well-informed of gossip and rumour. Her palance, also, is in a forgotten and out of the way place. It is very hard to play the "he sent messengers to every noble house" card when A) he did no such thing, b/c she would have heard of it and B) she chose a base that most people had forgotten about completely - part of the reasons she chose it was to have a place where she could control and monitor who she let in on her whereabouts
6) Finally, you discount that the exact same thing happened in Winter's Heart. Rand and Nynaeve suddenly Travelled near Shadar Logoth, channeled massive amounts of Power and Cleansed saidin. The whole point of this section of the book was to show how alien Rand was becoming to Min, Nynaeve and his friends - at this point, I doubt it even occurred to him that she didn't need to know what he planned to decide that it was time to run

I'm sorry, but maybe I'm too used to this series, but almost nothing happens in a straightforward way. In fact, I'm more convinced she is alive because it is so basic and elemental that there are a lot of "human" holes in the plan. Considering how good she is at self-preservation and her personality, I almost thing it strains belief to think she'd allow someone to come onto her doorstep uninvited when she is not the one sending the invitation. Personality is very important here - I simply don't think she is the type of villain to stay in her palace under these circumstances.

I could be wrong, but there are quite a few theories that seemed so basic as to be unassailable in their logic, only to have them turned on their head when a perfectly valid plot point based on personality and placement in the story is introduced. We'll see!