I guess I should have asked for clarification on what he meant by the "improbable conclusion" that the counterfactual mugging suggests. I thought he meant that the possibility of being counterfactually mugged implies the conclusion that you should pre-commit to paying the mugger, and not change your action based upon finding that you were on the losing side.

If that's not the case, we're starting from different premises.

In any case, I think the salient aspect is the same between the two cases: it is optimal to precommit to paying, even if it seems like being able to change course later would make you better off.