And yes, these two situations are equivalent, except for what I want the offerer to do, which I think is what yields the distinction, not the concept of a baseline in the initial offer.

Yes, the distinction is in the way you prefer to acausally observation-counterfactually influence the other player. Not being offered a trade shouldn't be considered irrelevant by your decision algorithm, even if given the observations you have it is impossible. Like in Counterfactual Mugging, but with the other player instead of a fair coin. Newcomb's with transparent boxes is also relevant.