It isn't making a move that I suggested was equivalent to making a binding commitment. (In this case, it's working out one's best strategy, in the presence of a perfect predictor.) It's equivalent in the sense that both have the effect of narrowing the options the other player thinks you might take. That's not a good notion of equivalence in all contexts, but I think it is here; the impact on the game is the same.

Yes, there are situations in which UDT-as-understood-by-the-OP produces predictable results. That doesn't mean that UDT (as understood etc.) Is consistently predictable, and it remains the case that the OP explicitly characterized the UDT-using agent as a superhumanly effective predictor.