It kind of seems to me like this debate is getting into self-identification versus defined identification. Games will define themselves as "FPS/RPG", but that doesn't technically mean they are an FPS/RPG. They could just have a really cool upgrade system. Likewise, a game may not call themselves an RPG, but have all the marks thereof.
Personally, one of the main differences that marks a role in an RPG to me is that I come to accept my role, rather than being told to accept it. It's the difference between Gears of War and Halo going "You're X. You will act like X, make all the same choices as X, and the story will progress the same way it would progress for X, because you are X. Don't worry, it's all taken care of. Just do X sort of things." or in Baldur's Gate or any of the other RPGs I play, me going "I am a complete tosser. I will act as such, I will shoot people in the groin, I will talk NPCs into killing each other, and if necessary, I will commit genocide, because that is what a complete tosser would do and that is what I am."
It's the idea of letting me accept and build a role that I can play instead of dropping me into a role and saying "Do this, because you are this." Some games are better at it than others, and to my understanding, those games are RPGs. F'rinstance, Diablo tells me "You're a Ranger!", whereas Oblivion (which is one of my big examples only because I started playing it again*) allows me to say "I am a master criminal, serial killer, and assassin. My main trademark is that I steal all the good wine from the wine cellars of my target before I strike." Granted, the game doesn't offer any benefits for this, but it allows me to define and accept my role, rather than letting me make one choice and setting me on a fixed path based on that choice.
But hell, for all I care, we can just name these games "Murray" or "Maurice" and redefine things to the point that RPGs become the useless metagenre they're slowly limping towards.
*I only have a refitted laptop and I can't load much except for TES and casual games. I needed my fix, and there ya go.