Do not get hung up in it.
If you go to showcases, play on a Showcase Team, etc. it really makes no difference if you go to private school.
BJ upton, the 2nd draft pick a few yeqars ago went to a private school, so did A-Rod if I'm not mistaking. My son attended a private school and is playing college baseball. The conference which he layed in average 8-10 players going on to college to play.