With the simulation requiring higher fidelity the more accurate it has to be. For a perfect simulation, the involved components would need to be perfectly mimicked.
This is false, unless you're also expecting perfect precision, whatever that means. Omega is looking for a binary answer, so probably doesn't need much precision at all. It's like asking if the cannonball will fall east or west of its starting position - you don't need to model much about it at all to predict its behavior perfectly.
how else would that belief of Omega's be justified
Nobody claimed that Omega's beliefs are justified, whatever that means. Omega doesn't need to have beliefs. Omega just needs to be known to always tell the truth, and to be able to perfectly predict how many boxes you will choose. He could have sprung into existence at the start of the universe with the abilities, for all we know.
If the universe is deterministic, then one can know based on just the starting state of the universe how many boxes you will pick. Omega might be exploiting regularities in physics that have very little to do with the rest of your mind's computation.
Just developing my second idea at the end of my last post. It seems to me that in the Newcomb problem and in the counterfactual mugging, the completely trustworthy Omega lies to a greater or lesser extent.
This is immediately obvious in scenarios where Omega simulates you in order to predict your reaction. In the Newcomb problem, the simulated you is told "I have already made my decision...", which is not true at that point, and in the counterfactual mugging, whenever the coin comes up heads, the simulated you is told "the coin came up tails". And the arguments only go through because these lies are accepted by the simulated you as being true.
If Omega doesn't simulate you, but uses other methods to gauge your reactions, he isn't lying to you per se. But he is estimating your reaction in the hypothetical situation where you were fed untrue information that you believed to be true. And that you believed to be true, specifically because the source is Omega, and Omega is trustworthy.
Doesn't really change much to the arguments here, but it's a thought worth bearing in mind.