Very precisely.  You think that shouldn't matter?

That is also why db's framing ("they give you 5000$ and I get to say how much you pay me to keep the rest") makes the problem subtly different, even though the underlying reward matrix remains identical in monetary terms.

I have insisted you don't necessarily treat this as a game theoretical abstract problem where utility is perfectly encoded in the monetary payoff and your job is just to maximize that.  That is, not unless that's honestly how you would frame it in real life.

The purpose of the thought experiment is exactly to explore how real human emotions and perceptions, and how real social dynamics, transform a problem which otherwise (that is, in an abstract game theoretical formulation) would have a clear unambiguous solution, invariant from all the different framings that maintain the same monetary reward structure.  That is, to explore the difference between rationality as formally defined in game theory and what makes sense to you in real life.

Whether you choose to call the latter "rational" or not is a matter of definitional nuance and not the main point.