Calling someone a douche is a pretty ambiguous charge - "frat" is the descriptor here.
When a person subscribes to a certain subculture, they tend to exhibit behaviors that are characteristic of that subculture, can we not agree? Some frats promote obnoxious behavior, which steals the spotlight to us "geeds"; it's a case of the vocal minority serving as the paragon of frat culture instead of the silent majority (non-douches). When a person's behavior falls in line with that stereotype, we use the "frat" descriptor because it is illustrative - not because we're implying that the stereotype is an accurate representation of all frats. I've called plenty of non-frat kids "frat douches" because they acted in line with that stereotype: excessive pride that impresses nobody other than their own ilk. Although I must say, for how much flagrant pride those vocal few have, they're suspiciously sensitive to criticism...
You know how there are guido douches, skater douches, art douches, etc.? Well, there's also greek douches.