Well, we know they are correlated. There might be a causal relationship as well, but the first study didn’t address that. In fact the entire premise of these studies seem to be to show the correlation and expect the reader to imply a causal relationship.
None of the studies I have read so far have considered the relationship between parental intelligence and parental income, and the hereditary relationship between parental intelligence and child intelligence. How much would that explain the income group differences (yes I know we disagree on the SAT as an intelligence test).
By the way, did anyone extend this study to consider the Asian students and their performance by income? I would expect a flatter curve there, which if true, could be illuminating.