The issue with this study in the context of the OP is this study discusses middle class vs poor. The OP discussed high class vs middle class. The main assertion of those who have argued against the OP is that high class vs middle class doesn't matter. I don't think people have seriously argued that middle class vs poor doesn't matter.
Good point, though that's really just the summary from the magazine. The actual Hart-Risley study (which was mostly the basis for the passage I quoted) shows that the relationship between SES and achievement is fairly linear, as are the relationships between SES and the factors that lead to achievement. I don't have time to scan in the entire appendix of the study, but here is a quick snap from Hart-Risley:
