I'm a big believer in kids being a reflection of their parents, and I still generally believe that if private schools were all watered down with society's problems, then those schools would be just as ridiculous as the worst public schools. In fact, some private schools in voucher-crazed Wisconsin have already gone down this road, with government paying for the attempt to reform kids. Just look at the schools that have closed or probably should close.
Generally, however, one must assume that parents who bother to send their kids to private school care at least a little bit more than the ones who leave their kids to fend for themselves in a poorly-rated public school. Also, a private school will generally have more options for throwing kids out. For the school and other kids, that's actually a good thing, regardless of how you see the the whole practice philosophically.
In six months of living in Jacksonville, there have been several major mistakes by students caught on film and used in local news. Twerking during class at a middle school. Fighting during a high school pep rally. Another fight at a middle school. All recorded and shared. All look terrible for the schools. All mostly a reflection of the parenting of the kids who acted like fools and those who recorded those fools.
The hope of parents who send their kids to private schools is that these kids never get sent to their schools. If those kids do show up, the hope is that they get thrown out before anything too bad happens. And since there's real competition in private schools for tuition, those schools DO throw kids out who cause problems, and they SHOULD.
You can sit around and lament the past, hoping that society improves, or you can send your kids to a more elite school, where kids behave in a way that allows them to not get sent to a public school.