If the subject is a contrarian, the desired X doesn't exist. But this doesn't prevent the GLUT from predicting all actions correctly.
We are imagining the following GLUT entry:
"The subject is presented with evidence E and the [possibly false] fact that the predicted action for this entry is X" -> The subject will do action Y.
X need not be equal to Y. It may be that there is no X for which the predicted action Y equals the action X that we told the subject we predicted.This is trivially possible if the subject is a contrarian who will always do the opposite of what you tell him he will do. But the GLUT is still completely accurate! We simply lied to the subject about what the GLUT predicted. We told him we predicted he would do X on being told he would do X, but actually we knew he would do Y.
Sure, but that's equivalent to just not showing him the GLUT in the first place. All you've done is move the problem one level up. There is still a circumstance in which the GLUT cannot reliably predict his action, namely that where you show him an accurate GLUT.
Suppose I have an exact simulation of a human. Feeling ambitious, I decide to print out a GLUT of the action this human will take in every circumstance; while the simulation of course works at the level of quarks, I have a different program that takes lists of quark movements and translates them into a suitably high-level language, such as "Confronted with the evidence that his wife is also his mother, the subject will blind himself and abdicate".
Now, one possible situation is "The subject is confronted with the evidence that his wife is also his mother, and additionally with the fact that this GLUT predicts he will do X". Is it clear that an accurate X exists? In high-level language, I would say that, whatever the prediction is, the subject may choose to do something different. More formally we can notice that the simulation is now self-referential: Part of the result is to be used as the input to the calculation, and therefore affects the result. It is not obvious to me that a self-consistent solution necessarily exists.
It seems to me that this is somehow reminiscent of the Halting Problem, and can perhaps be reduced to it. That is, it may be possible to show that an algorithm that can produce X for arbitrary Turing machines would also be a Halting Oracle. If so, this seems to say something interesting about limitations on what a simulation can do, but I'm not sure exactly what.