There are many things people refer to as "immersion". Sometimes folks mean it is like being immersed in reading a book, and for a while you lose conscious awareness of the outside world, or even that you are in the process of reading at all. Sometimes folks feel it refers to dropping deeply and emotionally into character, and so on. Overall, it seems to broadly refer to a state of focus or concentration on things going on in the game, rather than the outside world. Breaking immersion is then breaking concentration.
The idea that the player is the only thing that determines if that concentration can happen would need far more support than you are giving it. If a kid sneaks the aforementioned wiffle bat into a movie theater, you don't blame the rest of the audience for not being able to focus on the movie.
Instead, I would say that no single element "brings the immersion" - there's a lot of elements that can contribute to folks being able to reach the state of focus. The player matters, sure. But the other players at the table matter. The GM matters. Other things going on in the environment matter. And the ruleset matters too. That the interplay between these elements is complex and somewhat unpredictable does not mean that we, or game designers, should just heap it all on the player and ignore how what we do (or write/design) can impact results.