Maybe Omega [...] doesn't want it to happen [...] Moreover, you should be able to figure out that Omega would precommit

(Emphasis mine.)

I don’t think, given the usual problem formulation, that one can figure out what Omega wants without Omega explicitly saying it, and maybe not even in that case.

It’s a bit like a deal with a not-necessarily-evil devil. Even if it tells you something and you’re sure it’s not lying and you think you the wording is perfectly clear, you should still assign a very high probability that you have no idea what’s really going on and why.