This seems to be an old question, but it came to to the top of the list. I would say, yes charisma should play a role in deciding the reaction, but how to handle that and to what degree depends on a couple of factors.
1. Which system are we talking about?
Some systems very explicitly deal with social skills and even "social combat" and others do not. I would always say charisma or similar should play a role, but in exactly what way and to what degree depends on the system.
2. Does the player want the character to literally say what he said, or to get that idea across?
If they just want to get that idea across, then there is more room for the dice and character to step in and make the players actions work. You may be dealing with a somewhat socially inexperienced player who is playing James Bond. The player may not know the right words to say to get the idea across inoffensively, but James Bond could probably insult the other person horribly and make them like it, or enrage them by giving them compliments. And really, I think this makes sense. I certainly don't know how to make a fireball, but many of my characters do, why shouldn't one of them know how to deal with people far better than I do?
If they really want those exact words, then its harder. I still think charisma should play a role (it does in real life), but now there is less room for interpretation. I would still take charisma into account, but there might be penalties involved.
Essentially, I think someone with an exceptional high charisma should have all in-person social interactions seen in the best light possible, that seems the best anology to what happens in real life.