I think that's an America-centric view. In a lot of places in Europe it wouldn't matter what neighborhood you lived in - the schools available would be equally good.
It's not event an America-centric view, it's an urban America view. Live in a district that has only one school for each grade level, and suddenly the rich kids and the poor kids get the same education opportunities. I personally believe that's one of the reasons the upper midwest consistently has the best overall ranked schools in America.