From an interview I did a long time ago (in CT years) with Peter Brotzmann. It bolsters Jim's point, not my own, and I should've revisited it before posting.
AAJ: Do you consider yourself a jazz musician or not?
PB: That's a good question, and of course one that's not easy to answer. This came up before, I remember it very well. I was sitting with Cecil [Taylor] in one of those Berlin nights very long and we discussed [it] and he explained to me why he hates to be called a "jazz" musician. And of course, there's no definition actually. So if you're using this music in selling sausages or selling beer, or in German-TV crime series, or some kind of pseudo-jazz based music, then don't call me a jazz musician. But if jazz means [being] dedicated to the instruments, to your comrades you're working with, to the people who invented this kind of music, to the history, or just to a man like Coleman Hawkins who played so great on this horn, then I would be proud to be called a jazz musician. But, if it has to do with Lincoln Center and this [Ken] Burns guy, and Michael Dorff and all that crap, I don't want to have to do something with that. But, if it comes out of the tradition or the real meaning of the music, if somebody would call me a jazz musician, that would make me a little proud.