Not disagreeing outright, but there are studies[1] that link high-poverty areas with higher lead concentrations. There was also an interactive map, some time ago, that showed lead soil levels by zip code and they definitely seemed to match up with more problematic neighborhoods. Clearly, the factors you call out have an influence, but lead seems to be a part of that equation.
[1]: http://www.ncbi.nlm.nih.gov/pubmed/22752852
Edit: switched low with high.