I agree that local property taxes aren't the whole picture but they determine _quite a bit_. I know kids who grew up in more middle (or higher) class neighborhoods had higher property tax values and didn't suffer many of these problems as a result. As it is growing up in the hood was a pretty harrowing experience, but let me tell you that I did not look forward through trudging through sand into a trailer to take class by an unmotivated teacher who just wanted to clock out. Sure American education is still horribly patch-worky and quality is highly determined by local government policies, but there's a base level of dysfunction that can be solved through funding schools outside of property taxes.
You can talk all you like about the other factors that affect the quality of educational outcomes in a given school (district), but if basic infrastructure like those I've cited from TFA is not functioning, the other factors don't really make a lot of difference.