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EHeller comments on Newcomb's Problem and Regret of Rationality - Less Wrong
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The point here is that the question is inconsistent. It is impossible for an Omega that can predict with high accuracy to exist, as you've correctly pointed out it leads to a situation where Omega must either fail to participate, refuse to participate or cheat, which are all out of bounds of the problem.
I don't think it's ever wise to ignore the possibility of a superintelligent AI cheating, in some manner.
If we ignore that possibility, then yes, the question would be inconsistent; which implies that if the situation were to actually appear to happen, then it would be quite likely that either:
Since it is far easier for Omega, being an insane superintelligence, to cheat than it is for someone to cheat Omega, it seems likeliest that if anyone is cheating, then it is Omega.
After all, Omega had and did not take the option to refuse to participate.