[barrkel]

It sounds like you heard "causation" when parent said correlation. Correlation is observed in past samples; what you describe is a mechanism for trying to disprove causation, but it won't remove any correlation from the past samples, and it probably won't remove the correlation with historical wealth of the family etc.

[smsm42]

Parent said "primary correlate". Primary implies some special-ness, that is not like the others.

I do not see any way "historical wealth" could directly - without intervening variables - influence one's SAT scores. Of course, having affluent parents may mean certain value given to quality education, certain amount of care and access to development tools and so on - but then those should be primary factors considered, not wealth per se.