After having three go through the Great Neck South district I'd have to disagree with you.
I attended a very exclusive private school in Old Westbury and the same intellectual sloth you find in Hempstead High can be found there too. The difference is that in Old Westbury the parents have money to save the wee ones from their stupidity.
Of course, the more ambitious (and we hope talented) teachers will always be more attracted to the schools with better quality students, so to a certain extent, these districts will have better teachers. However, for the amount of money people in Millburn or Great Neck pay in property taxes, I could send my kids to private school.