But if instead Z exists, shows up on your doorstep and says (in his perfectly trustworthy way) "I will take your money if and only if you would have given money to Omega in the counterfactual mugging", then you have evidence that Z exists but no evidence that Omega does.

The point is that you need to make your policy before either entity shows up. Therefore unless you have evidence now that one is more likely than the other, not paying Omega is the better policy (unless you think of more hypothetical entities).