Absoulute nonsense take. What is being said affects the DC, or at least it should if you understand how DCs are actually supposed to work.
Do you do puzzles in your TTRPG? If so, when a player figures it out, do you then ask for an intelligence roll and if they roll low you go "Hmmmm (comes up with a reason for it not to have worked) sorry you failed"?
Do you have something like a trap door hidden underneath a rug and if a player says "I'd like to pull up the rug and see if anything is there"? and then say to them "Ok, I know you said you'd like to do that, but please roll investigation first. Oh noooo, so sorry, you CAN'T pull up the rug because you rolled too low."?
What the players choose to do and say with their characters can remove the need for a roll altogether. Similarly, what they choose to do can be impossible no matter how high you roll.
If you are caught in a castle and a guard questions you, saying you were there at the behest of a real named NPC will be MUCH EASIER (or even an auto pass situationally) than saying you've been a servant there for 20 years, and saying "Actually, I'm the king" should be impossible no matter how high you roll.
It's not because the player was good at voice acting, it's because he chose the perfect tack for his explanation that perfectly fit with the biases of who he was speaking to as well as fit with their knowledge. He wasn't speaking to a random NPC, he was speaking to a relative about his actions of the past week (trying to keep this spoiler free as much as I can).
Critical Role's Brennan Lee Mulligan ditched D&D's dice in Campaign 4: no roll needed because a PC monologue was "too good."
Performance now overrides actual gameplay.
This isn't D&D. It's scripted celebrity theater pretending to be gaming.
They. Don't Really. Play.