No disrespect here because actually your quote is quite uninformative. You apparently take everything to be literal. "Private" does not mean "not in public view." read the entire Lee case and you will see why prayer was prohibited in that instance. Clearly it was school sponsored. This is not, it really doesn't get any simpler than that. A public school student who wishes to pray in private prior to his meal may do so at the lunch table. He or she does not have to go out of sight, pray and then come back to the table. Much like these students who will share a private prayer in public sight. You have a right to leave the premises during the private prayer if you choose, or you may get caught up in the moment and choose to join the kids, your choice.

Thanks for playing.