I agree with Talozin's initial post. To expand...I think there is a *degree* of this present in any game, but I think that the degree depends both upon the GAME and the PLAYERS.
Example (Game): I don't care what anyone says, Call of Cthulhu is less about empowerment than D&D, or you're fucking doing it wrong. Likewise, playing a Standard Heroic (75 Base Points/75 from Disads) Hero System Campaign is less about empowerment than a Standard Superheroic (200 Base Points/150 from Disads) Hero System Campaign, even if the characters in the former are more capable and competent than the PCs, and there is a *degree* of power fantasy involved even in the former. But pretending to be Indiana Jones is a different kettle of fish from pretending to be Iron Man, power fantasy wise. They're both better than you, but the former still needs to be fucking afraid when people shoot at him because bullets make him die instead of bouncing harmlessly off.
For instance, I have always played Shadowrun as much more about being clever and overcoming overwhelming odds than a straight power fantasy where you are some of the biggest badasses in the setting (you aren't, or you are doing Shadowrun wrong: Shadowrun is a cyberpunk dystopia, so while you may be a huge badass, the corps will always be able to swing more force to bear than you can, and however you fight (magic/tech/guns) you have to fight *smart*).
Example (Player): To some degree, my friend John will make ANY game he is playing in about the cool shit his character can do, and being a badass, even if the campaign is a horror campaign about helplessness, dis-empowerment, and fear. System has very limited mitigating effect on this.
Having not playing Paranoia I have no idea if you're just a normal person in it, but the vast majority of RPGs make you a person of considerable power.
Paranoia definitely has zero aspects of power fantasy. Of course, Paranoia is kind of...the opposite of virtually all other games. Although I mean sissy indie/story/microgames mostly aren't about any kind of power fantasy either, they're about gay cowboys eating pudding, but Paranoia is an interesting example of a AAA game that totally isn't.
Lesson learned: we have a word filter.
It's from my time over at the IKRPG forums. A few posts above I say basically the exact same thing as Silva linked and when people argue it I challenge them to describe their last character and tell them they will probably focus on the ways in which their characters are powerful and exceptional. The response is a guy simultaneously declaring that he doesn't enjoy feeling powerful while LITERALLY describing the character he likes to play as a Cool Guy who Don't Look At Explosions. He literally describes lighting cigars on the burning clothing of his dead allies while striding away with an arrogant smirk and uses this as proof that he doesn't use roleplaying as an escapist fantasy.
Well there ARE actually some people that are equally/more interested in their character's weaknesses over their character's strengths. Like, they DO exist. The person you were talking to just did a fucking awful job of pretending to be one.