Sure. And no one is disputing the notion that smart people can succeed wherever they go. Also, Sayreville was, at the time, a pretty damn good public school if you were in their AP curriculum.
But in the 1970s, if you were really smart in the Sayreville school system the first thing you had to learn was how to defend yourself because some of those kids were pretty brutal. One possible argument in favor of private schools is that you don't have to put up with ridicule just because you know all the correct answers on the test.
Parenthetically, I would also argue that having to learn to defend yourself against people who seek to abuse you simply because of who you are isn't a bad thing, either, but that's probably off the topic.
It's true - smart kids can be successful anywhere. But, as
@vkj91 has pointed out, if you have the means to send your smart kid to a school where there's nothing but other smart kids, why not do it?