Ovinomancer gave an example from Burning Wheel where the outcome is based on a Duel of Wits. That is not a roll. It's a whole resolution framework, which first involves posting stakes on each side, and then a series of declarations and resolutions of actions, and can produce any of a range of results including various sorts of compromise.
I've posted multiple actual play examples, lengthy ones, from various systems: BW, Prince Valiant, Cortex+ Heroic being used to play MERP/LotR. I've posted them twice for good measure! I've also provided links to 4e D&D actual play reports, and have given summaries of some emotion/social-related stuff from Rolemaster play.
If someone described the D&D combat system in such a fashion as to give the impression that they think a character turning their back on an Orc and leafing through their shopping list can kill the Orc, do you think that would be a fair and reasonable characterisation? Or would it suggest a fundamental misunderstanding of both (i) the process of D&D play, and (ii) the sort of fiction that typically emerges out of D&D play?
@Oofta's characterisations of social mechanics are of the same quality and accuracy as my characterisation of D&D combat in the previous paragraph.