My boss I currently work for was a consultant for a couple of local professional sports teams. From my conversations with her, it definitely wasn't something just happened right out of PT school. It took a long time to develop a reputation and relationships with the various physicians in the area. Anyway, some of the orthos she worked closely with were part of Kerlan Jobe, the clinic in LA where a lot of pro athletes get treated at. The KJ doctors would often send pro athletes to her for their rehab assignments. As she treated more and more athletes, she developed a reputation and was asked by teams to serve as a consultant. As a consultant, she often treated many of the players but also maintained her private practice (exactly like how Minndasota put it). Aside from being an excellent clinician, it's about who you know and luck.
From my personal experience as an aide, I'd rather work with a Medicare patient over an NBA player any day!