I think the use of “FIRST,” means the author wasn’t saying “ALL that’s needed”. It is one factor listed in the post you quoted.
I can’t speak to the rest of the country but in Ohio the wealthiest districts are, generally, the best. Whether that’s due to their willingness to pass levies to fund schools or the fact that their kids eat well, read books at home, have educated parents, don’t have to have metal detectors or dodge bullets walking to school or whatever, is part of the debate.
We live in one of the best districts in the state and we do pay high property taxes for it. Also housing in general costs more here than it does 5 miles down the road in a poorer district where dropout rates are high and few kids go on to college.