There’s a committee, which includes but isn’t limited to the coaching staff. USA Basketball has a board of directors with representatives from the NBA and NCAA, headed by Jerry Colangelo, the former owner of the Phoenix Suns and a respected personnel guy.
The way the team gets picked is that the committee puts together a pool of worthy players – say 30 or so – and that’s the official roster for about a three year period, leading up to the world championships and then clear through to the Olympics, so there’s some continuity and familiarity. For every actual competition, depending on injuries and how the team has been practicing and who the coaching staff thinks looks good and whatever else is going on, the twelve-person active roster, which you have to register according to that competition’s rules, is picked from that pool. For the Olympics I think USA Basketball technically only nominates the players, and the USA Olympic Committee or whatever it’s called actually does the official choosing. There’s also a separate team, the Select team, the purpose of which is to have people around to practice against the active USA team; the Select team has tended to be made up of younger guys who haven’t really established themselves yet but who the coaching staff wants to take a look at for future competitions.
As far as whether basketball is an anomaly or not, it isn’t. It is a team sport, though, which means there can’t be an automatic qualifying process, which does make it a lot different from a lot of sports. You can’t just have everybody play each other one on one and take the twelve guys who win, so there’s a lot more subjectivity than there is in track and field or something. But the process for soccer or hockey or gymnastics is pretty similar.