My grandmother dies and leaves me $5000 inheritance. You are my next-door neighbor. You ask for some of the money. I say "sure, I'm feeling nice here's $10". Do you bash my $5000 car with a hammer because I didn't give you enough?
It's harder to think of a scenario that is less analogous to the game than this one. You're missing the point entirely.
How is it different? Because in one case there is a "rightful" owner, and the first case, the money appears to be "shared" at one point in time?
Well, I can't respond for anyone else. I can only give you my opinion and subjective values. And besides, this is somewhat of a red herring to the fact that rejecting an offer in the game is not irrational under any circumstances.
Anyways, I personally would find that:
1. You have a legal claim to the entirety of the funds
2. You are not obligated to make any offer to me
3. You are not receiving the funds under the condition that I accept a one-time offer that you are obligated to make
So no, I wouldn't personally smash your car. I would reject your $10 offer in the game.
Fair enough, but the result is still the same in both cases.
Do you feel like you were obligated to some amount out of the game?