My ideal is that you and your character share the same thoughts. I don’t want to pretend to be intimidated by an orc that I know I can kill without breaking a sweat, because the dice told me to. I want to genuinely be intimidated (on my character’s behalf) because I don’t know what the DM is up to.
If there is no threat, a DM might decide not to call for a check. Right?
Generally though, to my reading everyone is okay with there being game mechanics that do decide what a player character thinks, says, or does. All or almost all are okay with PC ability checks deciding what NPCs think, say or do. Many though are not okay with NPC ability checks deciding what a PC thinks, says, or does. And analysis of RAW diverges on that score.
I think the social skills are deception, intimidation, persuasion, possibly performance, and by implication insight. Deception seems to get a pass for NPCs to use it, because it can be looked at as not changing what a character thinks. I don't share that view, but perhaps it doesn't matter. Insight also gets a pass. I think it likely that many cases involving performance by an NPC will also get a pass.
So we are concerned only about intimidation and persuasion. There are I think valid concerns about the balance of permitting them to be used to override what characters think. Here I intentionally say characters because - thinking of
@Lanefan - the power they might confer NPCs is a mirror of the power they might confer to PCs. In fact, I would say that power risks far less disruption in the hands of an NPC! In play, I have seen the social interaction structure in the DMG prove very poorly balanced, so I have a strong sympathy with concerns around the balance of these skills.
Further efforts to settle the legal arguments are likely fruitless unless someone introduces new thinking. Therefore I want to focus more on what happens if - for the sake of argument - intimidation and persuasion were something NPCs can use. That has speedily turned up worthwhile considerations.