I do think there's something to what JO says. I don't know that I would put it in such metaphysical terms, but I think a lot of roadies and mountain biker's view the bicycle as a piece of sports equipment or a toy. Cycling is a thing they do and in order to participate in that sport one must have the proper equipment.

On the other hand, there are cyclists for whom that is an identity. They don't have a bike, they're a cyclist. A person doesn't usually need a lot of kit to be themselves. I propose that many who choose to ride fixed gear are just such people.

Edit: Oh yeah, and I do stop for every cyclist I see sitting on the side of the road. Most of the time I have what they need to get them rolling again. Once I was even in a car but I had my tools in my bag. It was at night and I think dude thought I was threatening him at first.