Not really - I live in lower Westchester and it is very common in the uber rich areas that they intentionally jack the property taxes way high to give to the public schools to create almost private school like qualities so they can write it off on the taxes and keep others out.
Its not race or class warfare - but the truth. Where I live - you have disasters like mt vernon, new rochelle, yonkers, peekskill, and then you have schools like scarsdale, pelham and bronxville two minutes away and its a drastic difference.