Simply saying 'you could share it with this guy' is not like the other case, because the two people haven't been called out as special. You don't share windfall with everyone you meet, why should this guy be different? In the DG, the other player was brought into the game and spent time waiting around just like you. It calls them out.
I'm trying to find a way of constructing a closely analogous situation without self-consciousness, and am having a tough time.
You don't share windfall with everyone you meet
I usually do.
Well, for some value of “share”, “windfall”, “everyone”, and “meet”, at least.
http://www.epjournal.net/blog/2013/05/are-all-dictator-game-results-artifacts/
Link to paper (paywalled).