Well it's private school, of course money is a factor. I'm not trying to be mean or anything but private school is pretty much known as "schools you pay a lot of money to attend." So if you can't afford it, it's no surprise you're not going to be able to go.
Also you can say "he gets 15k from each of the 500 students every year" to make it seem like he's pocketing it all, but he's not. He has to pay the salary of each faculty member and then pay the expenses of everything at the school. That's why private schools cost a lot, because they don't get the kind of funding public schools get. Now I'm not saying this headmaster isn't doing well financially, but he's not pocketing the entire tuition of every student each year; he's probably not living in some mansion.
Also, did said student's parents try talking to the headmaster and arranging something? Or did they just not pay and let whatever happened, happen? Students who make the school look good are a benefit to the school(ie when they go off to a good college or they do things in the world, people will trace him back to said school and the school can say "Ya, Bob went here. We helped him get to where he was." But if he was just a popular kid that doesn't necessarily mean he was a positive addition to the school. In public school many popular kids/well-liked kids are assholes.
On the otherhand I will dwelve deep down to my inner-child and ya, this **** sucks. It sucks being separated from friends and it probably sucks for the kid to be ripped from a familiar setting. It's hard for me to sympathize with kids who go to private schools considering the cost and the fact I was raised in a family with little money in a tough area in pretty ****ty public schools, but I know it's hard to look past the fact that most kids in school look towards friends to get through a school day.