I've always taken Omega to be just a handy tool for thinking about philosophical problems. "Omega appears and tells you X" is short for "For the purposes of this conundrum, imagine that X is true, that you have undeniably conclusive evidence for X, and that the nature of this evidence and why it convinces you is irrelevant to the problem."

In a case where X is impossible ("Omega appears and tells you that 2+2=3") then the conundrum is broken.