Okay, so let’s take an example. It’s silly, but I hope it’ll be something that everyone gets.
Rodney Dangerfield’s character in Caddyshack… is he a low Charisma character who somehow makes all his checks? Or is he a high Charisma character whose player has decided to play him as crude and obnoxious but somehow everyone likes him?
Is there only one answer? And if either is possible, then the question is “what do the stats really say about the character?”
I love this example! Al Czervik (played by Rodney Dangerfield) is extremely effective socially. It's clear the background characters find him funny and entertaining, even lovable. He's a natural leader and life of the party. The main impact on the plot of his
nouveau riche boorishness is to infuriate Judge Elihu Smails (Ted Knight), making him lose control on several occasions and eventually accept his challenge to play a golf match for a sizable wager. When Smails refuses to pay up, Czervik sends some thugs after him, telling them to "help the judge find his wallet."
So, in D&D terms, he's making several checks related to Performance (one-liners) and Intimidation (interpreted broadly as manipulation; seeing his uncouth behavior as abusive, this is basically how he operates). He also makes at least one attempt at Deception, when he pretends to be injured during the match because his team is behind, which fails to achieve his desired result of having it declared a draw. He then succeeds on a Persuasion check when he gets the main character, Danny Noonan, to agree to be his his substitute in the match, promising to "make it worth your while."
And yet, if you watch Dangerfield's performance, there seems to be little in the way of guile behind most of these actions. It may be a limitation of the performer; for all his truly enormous talent, Rodney Dangerfield wasn't what I would consider a great actor, but it's as if he just stumbles into most of these situations like a force of nature, prevailing through dumb luck. So it's difficult to say if it's natural Charisma that gets him through, or skill, or some kind of "lucky guy" class feature, or a combination of things.
If I was to try to play this or a similar character in D&D, I think he would be a Warlock, Pact of the Gopher, (warlock because
nouveau riche, i.e. his money/power was come by through "unscrupulous" means, in the eyes of old money) with some Bard thrown in for one-liners.