So far as I can make out, that misreads the wording in question. Those words define what it is to be roleplaying. They do not impose any constraint on the DM.
It's written definitively. This is what the player controls.
C: I fly over to where the dragons are and...
DM: Um, look, your character cannot fly, maybe if...
C: But don't I get to decide what my character does (points at PHB175)
DM: ...
C: Okay, well if I can't fly there I teleport to...
DM: Sorry, but you also do not have the ability to teleport, would you...
C: Right, I dematerialise the dragons from here then, by thinking at them psionically!
DM: ...
J: I fly over to where the dragons are and...
DM: Um, look, your character cannot fly, maybe if...
J: But don't I get to decide what my character does (points at PHB175)
DM: And you did. You declared that your PC was attempting to fly, but the rules only give your PC a walking speed and you've invoked no specific rule to beat that general one.
J: Gotcha. Well then I walk over and start climbing the mountain to get there.
DM: THAT you can do.
Later
DM: The dwarf claims to know nothing about it, but...
C: I want to know if he's telling the truth!
DM: Okay, you can use your Insight against the dwarf's Deception
C: That's not right - I decide what my character thinks!
DM: Yes, but - your Insight is pretty good and he's willing to answer your, perhaps if you just roll...
C: Nope, there's no uncertainty here, he's lying!!
DM: ...
DM: The dwarf claims to know nothing about it, but...
J: I want to know if he's telling the truth!
DM: Okay, you can use your Insight against the dwarf's Deception
J: That's not right - I decide what my character thinks!
DM: Sure, do you think he's lying or telling the truth?
J: Nope, there's no uncertainty here, he's lying!!
DM: Excellent. Are you going to act on that belief?
Much later, C finally encounters a dragon
DM: Okay, so you failed your Wisdom saving throw against Frightful Presence and..
C: Oh no, nope, no way. I decide what my character thinks, says and does, and my character is not frightened - it doesn't affect me. Chaaarrrrge!!!
DM: ...
DM: Okay, so you failed your Wisdom saving throw against Frightful Presence and..
J: Oh no, nope, no way. I decide what my character thinks, says and does, and my character is not frightened - it doesn't affect me. Chaaarrrrge!!!
DM: Specific beats general I'm afraid. You can roll to save or just fail it. Up to you.
In case doubts arise about this, I count 76 MM monsters with one or more of deception, intimidation or persuasion. Using DNDBeyond. Three pages of 20 monsters each, and one of 16. Example, Bone Devil, deception +7, or Adult Green Dragon, deception +8, persuasion +8.
Take out deception. That skill isn't at issue here. It doesn't make the PC believe or do anything.