My kids are at a non-sectarian private school and I agree with your assessment of some kids! These kids can run wild and who cares? I'd rather a responsible elephant-peekinese family than some we've got. That said, I support a private school's ability to expel anyone they chose. Just think the school might have been able to influence the girl positively had they chosen to.
I completely agree with their rights to expel whom they chose (even though I think they were, well, you know, hahahaha, for their reasoning here), that was part of the reason I chose to send my children to a private/parochial school. Unfortunately, I have found that they aren't as good at expelling as they should be. It is evidentally a monetary issue which just kills me since I am paying absurd sums for them to be doing the disciplinary actions in the first place.