Why does this bother you?
My groups always found these moments to be D&D comedy gold, and in the case of the dumb character/smart player, a chance to flex our storytelling muscle by trying to rationalize exactly how the idiot became a momentary savant.
Sometimes solving a puzzle is more fun than simulating solving a puzzle.
Yes, but isn't the entire point of role-playing actually playing a role? If the game forces you to step out of your role and allows, and even rewards you, for doing so, isn't that a mistake?
And, let's face it, I'm certainly not the only player to ignore the stats on my character sheet when failure means a high chance of PC death. That Cha 9 fighter suddenly becomes the most eloquent public speaker in history when he has to explain why his hand is down the bodice of the mayor's wife.
I find it very jarring now to have to ignore what's on the character sheet in order to play.
For our group "player skill" is essentially, "player's ability to group storytell" we don't care about system mastery or being the best in combat or knowing every little rule or anything of that sort. It is all about us all telling a story together, so the closest thing to player skill is how well you can storytell along with the rest of us. In a way even the DM has some measure then of "player skill"
This isn't a bad definition IMO. It pretty much incorporates the idea of metagaming without calling it such. After all, if you are group story-telling, you have to metagame to some extent. Like I said before, my problem comes in when the game pretty much ignores what's on your character sheet in favor of a "good story".
Situation #1: A patrol of the Town Watch surprises the characters skulking around the back of Lord Malintent's Villa.
Player Skill: "I tell them that we saw a shadowy figure holding a blade moving down The Street of Woodworkers, and we thought it might be the Leafydale Ripper. We want to catch him and get the reward [more plausible than an appeal to the goodness of our hearts] so we chased him back here, but we lost him [which could cast suspicion on Lord Malintent, who we think is guilty anyhow]."
Character Skill: "I roll a d20 for Diplomacy."
System Mastery: "I roll a d20 for Diplomacy. I make a DC of 58 or better."
Situation #2: The party discovers a hallway into the Inner Shrine of Mano-Tiki-Tia. The hallway is paved with tiles of three different colors and lined with statues bearing suspiciously hollow ports for their eyes and mouths. Skeletons, their bones nicked by stone darts, litter the hallway.
Player Skill: "Using my 10' pole, I probe one of the tiles. I'll start with a blue slate tile."
Character Skill: "I roll a d20 for Search."
System Mastery: "I roll a d20 for Search. I make a DC of 58 or better."
and so on.
Why do you equate System Mastery with powergaming? They are certainly not the same thing. System mastery simply means that you don't make substandard choices, not that you take advantage of possibly fuzzy rules in order to be more powerful than anyone at the table.
System mastery can be as simple as putting your highest roll into your prime requisite. It can be as simple as taking weapons specs for your fighter because it helps you do more damage. Taken to extremes, I suppose it becomes powergaming.
Same as player skill, taken to extremes, becomes pure meta-gaming. "Oh, that's a Fleagarbarf. They're weak against acid. Get out your vials boys!" is player skill. The player has memorized the Monster Manual and knows the weakness of every monster.