I fully agree, that sounds like the definition of - or, at least, a description of - immersion, to me.
Still holds no value to me.
I like and value role-playing: being aware that you are in a game, and focus on your character as if the game world were real. "How would Sara Landsknecht, if she were a real person, react to this situation based on her knowledge and personality?"
Or the (sadly) superior metagaming: being aware that you are in a game, and trying to focus on your character as if the game world were real, while still paying attention to out of character concerns. "How would Sara Landsknecht, if she were a real person, react to this situation based on her knowledge and personality? How will that affect the enjoyment of the group? What other options might she take that are still in character?"
I'll admit, metagaming certainly breaks something (concentration on role-playing?) that I'll call "immersion" at times.
If the logical thing for a combat-savvy character to do does not match the player's concept of the character's personality, then the player should strongly consider that they are at fault, for not making a character who "grew up" in that world. Fortunately, playing Quertus, my signature academia mage, for whom this account is named, I don't have to worry about "optimal" choices, as Quertus' general tactical ineptitude frees me to just roleplay his decisions correctly. No need for lost immersion.