I would guess that the problem is the word "immersive" is so broad as to be confusing.
When I play World of Warcraft (which I have started doing again because my son is old enough to play) sometimes when I jump my character off a really high cliff, I actually feel it in my stomach. I would argue this is because of immersion.
Alternately, if a GM were to tell me, "Wait, your character wouldn't know to burn trolls...you can't do that!" my sense of immersion...of the kind that I enjoy in RPGs...would come to a screeching halt.
But I don't think either of those types of immersion are even remotely the kind of immersion you are talking about.
So I don't think it's useful to use a term that can be defined so many different ways.