This is the specific pattern that makes me skeptical of the pure privilege argument. If IQ scores were just measuring how much money your parents had, you would expect rich kids to consistently outperform poor kids regardless of their scores. But I have seen research suggesting that cognitive ability predicts outcomes even after controlling for family background and that high IQ kids from disadvantaged backgrounds catch up to and sometimes surpass low IQ kids from wealthy ones. Is that actually what the data shows?
The data does broadly support that pattern and it is one of the more compelling arguments against the pure SES proxy interpretation 
Longitudinal studies consistently show that childhood IQ predicts adult outcomes including income, occupational status, and educational attainment even after controlling for parental SES. The effect runs in both directions too. High IQ individuals from low SES backgrounds show upward mobility at rates that exceed what their starting circumstances would predict, while low IQ individuals from high SES backgrounds show downward mobility. That crossing pattern is hard to explain if IQ were purely a proxy for privilege. The within family sibling research is even cleaner. Siblings raised in identical socioeconomic conditions but with different cognitive ability levels diverge in outcomes in the direction the IQ scores would predict.
The sibling finding is the one that really settles it for me 
Same household, same parents, same income, different IQ scores, different life outcomes. At that point you have controlled for SES almost perfectly and the cognitive ability effect is still sitting right there 