A weird but fascinating article on the topic of private schools:
Elite schools breed entitlement, entrench inequality—and then pretend to be engines of social change.
www.theatlantic.com
I know people whose kids go to private schools (most to one specific school) and the kids do have an 'air'. It could be called smugness, superiority or 'Miss/Mister High & Mighty', but they do extremely well, academically. This school is in a wealthy suburb and is secluded, but they also have kids from Milwaukee who would never be able to afford the tuition, too. They don't allow poor performance but the kids stay and they try very hard to succeed because they're taught that they're worth teaching.
I don't think any of these kids have earned poor grades, but I can think of at least one of the parents who might make the kind of call described in the article. He has become increasingly arrogant and annoying over the years, too.