I will give one example that shows why the claim is false. It is somewhat parallel to [MENTION=87792]Neonchameleon[/MENTION]'s examples around group membership and knowledge of friends/acquaintances.
I like to play religious PCs, and I currently have multiple PCs in my 4e game who are religiously fervent. As a player, when playing a religious PC, I also determine, from time-to-time, the will and desires of my god. The players in my 4e game do the same - eg "We can't do such-and-such because the Raven Queen's preference is for so-and-so."
The player is exercising a power to determine what is true in the fiction about his/her PC's god. The PC does not have any such power. Yet this does not reduce immersion in the character. Indeed, nothing is more debilitating, in my view, to immersion in a religious character, than to have to stop at every point and seek the GM's advice on what the religion does or doesn't permit: this produces the experience of a bare novice still under instruction while trying to roleplay a deeply engaged initiate