I'm using how roleplaying is defined in the rules of D&D 5e. It's just the player deciding what their character does, thinks, and says. Whether or not that aligns with somebody's notion of what the character might reasonably do given the context is irrelevant, particularly as anything can be justified in a game based on the childhood game of make-believe. If it does align with the character's personality trait, ideal, bond, or flaw, then that might be worth Inspiration.
But anyway, even if we did go with your definition, there's nothing about a dungeon that inherently prevents someone from "playing your character as a character." If you think that's not true, please tell us how.