Yeah. Going by the responses I've seen here, that's the case. I just have a very hard time understanding how someone who is living and breathing the character's life, emotions and thoughts, and struggling with that character's dilemmas, isn't feeling immersed.
I can understand how they might prefer a different form of immersion, but I can't understand how it's anti-immersive.
To give an example from a fairly recent game - it was a Ravnica based game and I was playing a law abiding Azorius functionary. As part of the characterisation, I decided to try and sure that the party didn't kill any citizens. I'd taken Spare the Dying as a cantrip and was delivering it by familiar to fallen NPCs who the party had been fighting with. The character had been doing pretty well with this and had ensured that everyone on both sides had survived all fights.
Due to some bad dice luck, the character was pushed into a situation where they had to chose between healing a fallen NPC and ensuring a party member was certain to stay up the following turn (I could predict from what we were facing that they were likely to, but I could ensure that they were).
In the end, I decided the character would keep the party member up - trading a momentary tactical advantage for the life of the NPC. This lead to a bunch of character development, interesting roleplay and so on over the next several sessions. However, in retrospect if I'd made the other choice and the party member had been dropped, it would have also lead to a bunch of development, interesting roleplay and so on, so it wasn't just a choice of "what was more interesting".
However, while I certainly felt immersed in the character at the time and the decision was a great dilemma, I was taking some meta-game considerations into account (Initiative timings, player party cohesion) and was making the decision not as a snap judgement call, but struggling over it for a minute or more, in a situation where the character was in a dark dank hole, but the player was in a nice warm living room.
It's the kind of thing that might have triggered a Humanity test in Vampire, a Compassion test in Exalted or something similar in Pendragon.
As it was, either way would have produced a fun game and I'd have learnt something about the character - making it by fiat has kind of sat badly since, it felt more like something done for meta-game reasons than being true to the characterisation. But the opposite choice may have also have felt like that in retrospect (We all know the potential risks of Its What My Character Would Do, and it was partly in pursuit of a self imposed OOC challenge). In this case, leaving it to fate would have removed the second-guessing