“College sports is big business, but not for the students” true however it is not simply a scholarship/stipend if you play football or basketball at a big time sports program you have a lot of stuff in the “win” column… local celebrity status, dreams of pro sports as a career (yes, I know most players do not wind up in the nfl or nba) lots of women interested in you, being on TV etc… and major breakouts become super famous before they even go to the next level. there is a massive draw to play football/basketball in major programs even if you are still a long shot for the pro sports.
there are some crazy stories like this one (med school/nfl at the same time)
http://www.espn.com/blog/kansas-city-chiefs/post/_/id/17958/chiefs-laurent-duvernay-tardif-leads-rare-life-as-football-player-future-doctor