Boys also aren't allowed to wear bikinis, and their swimsuits are (usually) shorts already.
No white Tees is BS though.
However, without context, I would hazard a guess that the summer camp has a religious affiliation (most do). My YMCA affiliated summer camp required that all campers attend chapel on Sunday. I "learned" the "hard way" that not participating at chapel was "punished" by being sent to the cafeteria to play games and eat extra breakfast with the non-christian staffers.