My experience differs, in that not knowing the rules/mechanics frees me up to just have my character (try to) do what it would do; and the GM can sort out the mechanical implications.
We see it differently, then; as I see "immersion" as - at its peak - describing the state where I forget I'm a player at a table and am thinking only as the character in the setting.
I agree with you, with the little exception that sometimes, "being a character in the setting" involves knowing the odds of some actions or the way the universe will deal with you the same way we as human beings outside of the game "know the odds" so we don't cross highways at night. It is, in my opinion, a fine line because if you "know too much of the rules" you stop behaving like a character inhabiting the world because you know the rules opens up more solutions than are genre-appropriate.
I'll try to make myself clearer:
If I know I have 150 HP and falling from orbit can do at maximum 120 damage, then jumping down the castle wall becomes a possible choice, even if nobody in the game world would do that, because every single NPC treats falling as a big danger. So in this case, knowing the rules (or thinking about them in the decision making) can threaten immersion.
On the other hand, if I don't know the falling rules, I could assume falling works the same way as in our world and people die falling by missing a step and jumping from a balcony expecting to land on a horse would result in a horse with a broken back and a hero with possibly broken legs. Or worse. But character in the world might be routinely be able to do that if the genre of the game is "The Three Musketeers" and the rules only ask for a very easy acrobatic check. In this situation, not knowing the rules precludes doing things your character would absolutely do. Detailed knowledge isn't necessary, but sometime knowing the genre being emulated can help immerse better in the character mindset.