I think Brett is enjoying the attention that his moping is getting him. Not saying he isn't actually depressed, or going through problems, but the fact that he does what I call the "Eeyore thing" of saying nothing is wrong, then continuing to act mopey, look sad, etc.. yeah, that's annoying. And I do agree it's a bit drama queen-ish. I'd quit asking, and basically ignore him unless he chooses to opt in to the gathering in a positive way.
Is it possible that the friends that are asking YOU about Brett are doing so to try to make sure that he's at least base-level okay (ie, not in an actual crisis) without having to be subjected to his hours-long monologues about his problems? If so, I'd go with "Eh, I think he's okay, just not having a great day".