1) If that happened, it would 100% not be the words that did it.
To me, it would be the words, if they were deceiving you into believing that they would go through with it, but had no actual intention of going through with it.
2) I could make the choice not to and take the risk. People do that.
Agreed. However, even self defense courses, they tell people in such situations to just give them the money, jewelry, etc. as material things are not worth risking their life.
A friend of mine was approached on Hollywood Boulevard by someone who demanded his wallet and showed him a gun. He chose to just walk away from the guy. Nothing happened. But it could have. He could have been shot. He made that choice. It wasn't made for him by the guy with the gun and the threat.
Yep. and apparently the person with the gun had no intention of following through with violence. Maybe, your friend was good at reading the person (sense motive vs deception).
When it comes to rpgs, most of the 100+ games I have encountered over the years have combat skills, athletic skills, knowledge skills, interaction skills, etc. which reflect the character's abilities not the player's abilities. Uncertain outcomes are resolved with die rolls-typically with opposed rolls (or saving throws) when two characters are in opposition (including combat, athletics competition, etc). I, therefore, don't see a reason why social interaction outcomes between characters should be any different. Ymmv.
edit: I do, however, also like mechanics that allow a resource for a bonus for players to alter roll, reward players for going along with failed social outcome, and/or allow GM to spend a resource to compel players to go along with failed social outcome.