I can see why it would seem strange that they would follow along, but I think there's enough in-world reasoning why they would go along with it for it not to seem out of place to me imo.
True, i dont think it's what she wants to to by any means, but the whole thing in the tower is they work to beat that kind of dissention out of the novices/accepted, make them learn to toe the line
My guess is because at that point they don't know that Aes Sedai (Black Ajah) can lie - they'd assume the 3 oaths held, so they'd assume, if she said something outright that it must be the truth
Plus they don't know she's black or that the black ajah even definitely exist.
As to her being...