After a while a wild thought ran through his mind: “What if every time a person looks at the proof of the theorem X, the Dark Lords of the Matrix alter the perception of this person to make the proof look correct, but actually there is a mistake in it, and the theorem is actually incorrect?”

As soon as the Dark Matrix Lords can (and do) directly edit your perceptions, you've lost. (Unless they're complete idiots about it) They'll simply ensure that you cannot perceive any inconsistencies in the world, and then there's no way to tell whether or not your perceptions are, in fact, being edited.

The best thing you could do is find a different proof and hope that the Dark Lord's perception-altering abilities only ever affected a single proof.

John searched through the meta-level controlling his thoughts. He was horrified to realize that Bayesian reasoning itself fitted the criteria: it was definitely organizing his thought process, and its correctness was implied by the theorem X he was currently doubting. So he was sitting, with his belief unsettled and with no ideas of how to settle it correctly. After all, even if he made up any idea, how could he know that it wasn’t the worst idea ever intentionally given to him by the Dark Lords of the Matrix?

At this point, John has to ask himself - why? Why does it matter what is true and what is not? Is there a simple and straightforward test for truth?

As it turns out, there is. A true theory, in the absence of an antagonist who deliberately messes with things, will allow you to make accurate predictions about the world. I assume that John cares about making accurate predictions, because making accurate predictions is a prerequisite to being able to put any sort of plan in motion.

Therefore, what I think John should do is come up with a number of alternative ideas on how to predict probabilities - as many as he wants - and test them against Bayesian reasoning. Whichever allows him to make the most accurate predictions will be the most correct method. (John should also take care not to bias his trials in favour of situations - like tossing a coin 100 times - in which Bayesian reasoning might be particularly good as opposed to other methods)