"Your Charisma (Deception) check determines whether you can convincingly hide the truth, either verbally or through your actions." So, seeing the overall definition of an ability check, it's not about whether the other party believes or does not believe, it's about seeing whether you can succeed or not at being convincing.
The charisma check never comes into play UNLESS doubt has been established. The check itself does not and cannot by RAW constitute doubt, or there would never be anything BUT doubt. The fact that charisma checks can be certain and need no rolls, means that certainty must established prior to a roll happening.
I have given you the opposite example, haggling using persuasion. In that case, it's an opposed checked and the DM determines the result.
Haggling can't force a PC to think anything, though. Nor is there a check unless the outcome is in doubt.
PC: I'd like to purchase this horse statue. How much is it?
Merchant: it's 25 gold.
PC: I'll give you 20 for it.
At this point as the DM I can have the merchant just accept that amount. Maybe the statue is only worth 5g and he was hoping for 12, but the PC's counter was so high that he'd rather just take it than argue further, so the outcome is in not in doubt. No haggling roll.
Alternatively, the merchant might have paid 20 and only had a 5 gold margin for profit and 20 isn't going to be taken, so he counters with 24 gold. If we get to a point where nobody is willing to budge through roleplay, but the merchant can still make a profit, I might determine that a roll is necessary, because the outcome of whether he will settle for 22 gold or not is in doubt. Success and the PC gets it. Failure and he doesn't unless he decides to change his mind and pay more.
At no point is the PC being forced to think or act, though.
I would argue that as a player, your reaction would totally depend as to whether I describe a whining goblin or an enraged pit fiend trying to intimidate you.
And an whining goblin isn't attempting to intimidate. If a goblin is going to try intimidation, it's not going to be by whining, so that's not a good faith description of goblin intimidation. But.....as a player my reaction would still be different if I were being intimidated by an enraged goblin or an enraged pit fiend. It would still be my choice, though. I'm just far more likely to decide my PC is intimidated by the pit fiend.
And yet, as a DM, I might roll the NPC's persuasion check to see whether he finds new information, or whether I can roleplay him more persuasive. Remember, I'm not rolling to see whether you accept the information, I'm rolling because I'm just not sure how persuasive my NPC is, it's only his success of failure on his attempt that I'm interested in.
Ability checks are explicitly only called for if the outcome is in doubt and failure has meaning. They are not under any reading of the rules called for just to see how persuasive you should roleplay the NPC. I mean, it's certainly a valid way to play it, but it's a homebrew method for ability checks.