Allowing for a margin of error, the simulation would indeed make do with lower fidelity. Yet the smaller the margin of error that is tolerable, the more the predictive model would have to resemble / be isomorphic to the functionality of all components involved in the outcome ((aside from some locally inversed dynamics as the one you pointed out).
Given an example such as "chess novice versus grandmaster", a very rough model does indeed suffice until you get into extremely small tolerable epsilons (such as "no wrong prediction in 3^^^3 runs").
However, for the present example, the proportion of one boxers versus two boxers doesn't at all seem that lopsided.
Thus, to maintain a very high accuracy, the model would need to capture most of that which distinguishes between the two groups. I do grant that as the required accuracy is allowed to decrease to the low sigma range, the model probably would be very different from the actual human being, i.e. those parts that are isomorphic to that human's thought process may not reflect more than a sliver of that person's unique cognitive characteristics.
All in the details of the problem, as always. I may have overestimated Omega's capabilities. (I imagine Omega chuckling in the background.)
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.