That's a strange term for it. How do the rules represent, for instance, tactical choices? Is there a process for deciding whether your character stands and fights or runs for the hills?
In the case of PCs, the player chooses. In the case of NPCs/monsters, there used to be morale checks for some of this, I think precisely to take it out of the realm of GM fiat.
But generally in D&D NPC monster tactical decisions
are a matter of GM fiat. Apart from anything else, this has been one traditional way for the GM to modulate the difficulty of a combat encounter - by pushing the NPCs/monsters harder or softer.
Is there a sympathy roll to determine whether you run to your fallen companion to heal him or attack the monster that killed him? It's admittedly a fuzzy distinction, but it seems to me that the rules don't generally address the exercise of free will. Which is pretty much what your average charisma-based check is supposed to be influencing, but not deciding.
Your sympathy example seems to be expressed from the point of view of a player playing his/her PC. In D&D, that can be resolved however the player likes (unless a group plays with extremely prescriptive alignment rules). In other games, it might be dictated by a personality mechanic of the sort that Nagol mentioned a few posts upthread.
Suppose one player chooses
not to have his/her PC heal another player's fallen PC. The two players can argue it out, not just at the PC-to-PC level but at the metagame level ("Don't be such a bastard!"). But generally the players aren't entitled to use the same sort of metagame-level arguments against the GM, at least in part because the GM's job
is, at some level, to be a bastard - to provide adversity.
So I don't find the comparison between player/PC-to-player/PC dynamics, and player/PC-to-GM/NPC dynamics, that helpful.