Actually, i would say what you are describing is a failed persuasion check - taking the wrong approach, directly challenging the belief.
The same studies found that while the counter evidence cases create the digging on heels, the finding common ground and more sidereal "common ground" did work.
So you might not be able to directly attack their big position directly but can get them to come to agreement on say a good hunting policy.
Same way folks can all agree on the individual elements of complex laws but be against it whencertain politicians name is on it - you work to the solo agreements.
Not unlike choosing to not frontal assault the castle but work a deal with a sude gate guard.
That said, yes, "can i be convinced of x" can be an absolute "no" - especially if the context is a single conversation or worse, a quick statement.
To me, one of the keys to skill use is time... How long are you going to work at it?
Want to seduce - takes time.
Want to get the king to like you - takes multiple things not just one quick line.
GM can choose the time requirement for various tasks that make sense... Nothing says Persuasion is always a six second task.
As a DM I certainly allow actions and skill checks to sway NPC attitudes, especially if it's over the course of time. In one of my last campaigns, I had the group start out as young kids. They interacted with a group of bullies but realized that one of them was being physically abused by their father (one of those throw-away-spur-of-the-moment comments on my part) and took pity on them. Didn't help them at that time, in fact it probably made things worse. But over the course of the years of campaign they always went out of their way to try to persuade the NPC through words and deeds that they weren't destined to become the force of evil their father wanted them to be. Eventually it worked. Screwed up a major plot point I had initially planned, but the NPC became an ally.
So yes the PCs can influence an NPC, especially over time. But in this case, it's because I kept an open mind on the issue and I try to see the world from the NPC's perspective. I decided as a DM that there was a chance of the NPC being influenced. Had the NPC been the physical incarnation of a demon, it would not have worked.
All I can say is that if a DM starts telling me what my character thinks or how they behave, I will object. If it's more than just a one time thing I'll find a new DM. Based on the reactions of my players when I miscommunicate and they think I'm telling them how they think or behave I'd say it's pretty common. Many if not most people I've played with don't want the DM (or other players) to run their characters.
Case in point: I don't think I can be convinced that character A should decide what character B thinks no matter how many postings there are on this thread, no matter how well the postings are written.
