High-status people feel like they deserve more, so it would be probably natural for them to extract as much value as possible, while "the bare minimum is good enough for me" would be a natural attitude of a low-status person.

That may be a factor, but that's one factor out of many.

Let me offer a similar argument but one that points in a different direction:

High-status people feel secure in their position so there's less pressure on them to "win" and they would be more willing to give up some stuff for warm fuzzies.

Or another one:

Rich people don't care about monetary rewards as much so in negotiations they would be willing to exchange financial benefits (the common subject of negotiations) for other things not usually measured as outcomes (time, status or, again, warm fuzzies).

I am not particularly attached to these two assertions, the point is the ease of making them and others like them.