Most good private schools have very little time for disruptive pupils - they know that there is nothing like a "problem" kid for upsetting the classroom and they usually have a long queue of parents desperate to get their kids in.
Which ironically means that the private schools get to bleed the public schools of their positive influencers and can shove all the discipline problems right back on the public schools.
From what I've seen kids who have a problem in private schools tend to either simply get shuffled around to another private school or end up in very strict boarding schools (often ones with traditional connections to the military).
You are correct though about private schools taking positive elements from the state school system - when you look at who typically attends a private school here the parents are typically successful, extremely motivated people who tend to pass these values onto their kids.
