Your first paragraph is based upon a misreading of my example. I said the private school doesn’t have a team.
No, I was just adding on to it.
If private school student wishes to plays sports for a public school that has his sport, then he’ll play in whatever school district the board assigns him to (probably the one he’s in).
BTW: i don’t know a lick about soccer but if they have it for AAU then he should go for that.