Nabokov has some things to say (in Lectures on Literature; worth reading) about expecting characters to be likeable/good guys. (He’s agin it.) Personally I don’t care whether my characters are “good” or not (though by their own lights they often are) but even if that’s important to a group of players it doesn’t rule out the facts-to-fit-the-evidence approach. They just have to genuinely believe they have intuited the real culprit. Wishful thinking will do the rest. I suspect this is how it works in most real-life miscarriages of justice.
I agree there is some ill-defined but very important distinction between what we think and say as player-characters and what the characters are physically capable of. I am happy to roll dice for sneaking about, climbing a wall, or hitting someone with a sword but, like you, I expect to figure out my own solutions to mysteries. Where it becomes a grey area is something like persuasion or oratory. I once asked a player to give the speech he was using to sway a hostile crowd, but he insisted on just, “I give a charismatic speech” and then rolling dice, on the grounds that his character was a skilled orator but he wasn’t. In those circumstances I don’t think I’d try to play the character unless I was willing to at least attempt the speech.
On one hand, this is a complete cop-out. As a player, go ahead and give an uncharismatic speech. The whole point of roleplaying, as opposed to storytelling, is to speak in character. Sure, your speech won’t be as good and will probably be abbreviated from the speech your character would give. That doesn’t matter. Even if you feel uncomfortable speaking in character, you can at least describe what the speech was about. If you aren’t giving us the words, at least give us the gist.
On the other hand, I get it. Not only is it incredibly difficult to play a charismatic character, but you may have other barriers to social interaction that prevent you from doing what I described above. If your ability to communicate comfortably stops at “I roll the skill check,” then we can be accommodating. The roleplaying table should be a safe space where you can try to exercise and develop your social skills.
Oh, that player has no difficulty in talking, believe me. IRL he’s an accomplished public speaker. He just couldn’t be bothered!
In general, I think it’s probably a good idea to play characters that fit your personality and comfort, a little like character actors being chosen for the types they’re good at portraying. That way the player can play to their strengths. Sometimes the strengths arrive through the character. I’m not good at fast-talk, for example, but if I play a character who is then I find the gab just flows as needed. A lot of the fun in roleplaying for me is in discovering things like that.