It might, again, have had a better chance of fooling Peranza if she hadn't been a minor player herself, for so long, in Cheliax's desperately struggling Conspiracy.
Peranza has seen what happened with Asmodia and her headband. Peranza has heard about Keltham's time-travel hypothesis to explain the strangeness there. Peranza has been told even about Keltham's Detected thoughts about how Conspiracy Cheliax wouldn't plot all that weirdness to talk him out of using a headband since they could have just not told him about Fox's Cunning in the first place.
And she grasps on an intuitive level, now, that when the Conspiracy is treating you one way consistently, and then suddenly switches to a totally different policy, the most likely reason is not that they have done something incredibly clever to fool you, but that things didn't go according to their plan.