In my opinion the original post (barring the later comment by the author) does not imply that Q is the same in the real world and in the counterfactual world. Am I wrong here?

Then, if Omega is a trustworthy all-powerful device, it would not construct a counterfactual that is straight-out impossible just to play a trick on me. Therefore I conclude that the counterfactual amounts to running an identical scanner another time and getting a different result. But now I no longer think that it is an independent copy of the scanner -- actually it is completely dependent (it is determined to return a different answer), so I no longer think that the conclusion about the coins is fifty-fifty, but that we shouldn't update.