In the context of an RPG, I consider "the game" to be the shared imaginary world. I consider "the meta" to be the real world where the rules and conversation about the rules are taking place. A player thinking about solving a task in the game world may or may not have any connection to the meta, and also the other way around. If the player isn't connecting the two, they are definitely not engaging with the game. It's a personal peeve of mind when a player specifically focuses on me the GM as the thing to be solved in order to succeed, as opposed to the problem posed in the game, and the process of convincing me that their character is qualified for the task very much sounds like engaging with me the GM rather than with the fiction. This sounds like the beginning of a game degenerating into GM wheedling as a central process of play, which for me wouldn't be fun regardless of which side of the GM screen I was on.