This is always so, there are details absent from any incomplete model, whose state can decide the outcome as easily as your decision. Gaining knowledge about those details allows to improve the decision, but absent that knowledge the only thing to do is to figure out what the facts you do know suggest.

If no facts about the nature of the "noise" is specified, then the phrase "probability of correct decision by Omega is 0.9" does not make sense. It does not add any knowledge beyond "sometimes Omega makes mistakes".

If people use this consideration to consistently beat Omega, its accuracy can't be 90%.

If only 10% of the people use this consideration, then why not?

(AFAIU, the point in parentheses basically amounts to the idea that in the absence of any known causal links I should use EDT (=Bayesian reasoning))