Your position was that a player decides how their PC acts and thinks independent of stats. That is not following the rules because it is ignoring and overriding the rules.
Can you quote the rule it overrides?
specifically stat values and the rules around resolution (like saving throws and ability checks).
But, by the rules, such checks and saves are made when the DM calls for them, not when players decide they want to force each other to make them.
A PC with an INT of 6 is going to think differently than a character with an INT of 18. Those values are important because they guide us as players in how to role play the PC. Choosing to arbitrarily ignore those and play your PC however you want is not wrong (see the above post re: having fun), but it does in fact ignore the rules.
Deciding to take your character’s ability scores into account when deciding how they think or act is certainly allowed by the rules, and in some cases encouraged by them, but it is never required by them. The only rule that governs how a character may or may not act is that the player decides how their own character behaves. Abiding by the results of rolls when the DM calls for them to be made is required by the rules, and at some tables the DM may call for rolls to resolve the outcome of PvP actions, while at others they may not. Neither ignores or overrides any rules.
Now,
my way of handling it, where the player, rather than the DM decides whether or not a roll is called for when their character is the subject of a PvP action is a house rule. It does differ from the normal task resolution rules. But simply saying that the player decides how their character reacts, and not calling for a roll, is perfectly within the rules.
Yes there are, by the very definition of what those stats mean, and what the values of those stats represent. I mean, "charisma" has a definition. And the value of that attribute means something, and tells you how your character comes off to others. That's literally a rule/guideline telling you as a player how to act.
There is no rule in the book that says that. If you enforce that guideline at your table, that’s part of the social contract of your games,, but it is not written in the rulebook.
What there are no rules for, is a rule that states "ability checks and saving throws no longer apply if it's another PC initiation the challenge." If I missed it, feel free to point out where it says that in the books.
On page 4 of the basic rules (I think it might be page 6 in the PHB, I don’t have the book in front of me), under How to Play:
”Sometimes, resolving a task is easy. If an adventurer wants to walk across a room and open a door, the DM might just say that the door opens and describe what lies beyond. But the door might be locked, the floor might hide a deadly trap, or some other circumstance might make it challenging for an adventurer to complete a task. In those cases, the DM decides what happens, often relying on the roll of a die to determine the results of an action.”
I would file “a PC tries to persuade another PC to do something” under one of those times when resolving a task is easy. Simply ask the player of PC being persuaded, “what do you do?” Since the player of the PC determines how their character acts, no dice roll is needed to resolve the action.
Those skill checks are there for a reason. If players always got to choose how they thought and acted, then why are there even certain skill checks to begin with?
For circumstances where the outcome of an action involving those abilities and/or skills is not easy and require a check or save to resolve. For example, when a PC attempts to persuade an NPC in a way that the NPC might or might not be receptive to, or when a spell is cast on the PC that forces a saving throw with one of those abilities.