I suspect the actual correlation is not with wealth (i.e. giving money so somebody with low SAT scores would not actually improve their scores - unless he would have enough money to bribe whoever is overseeing the test of course ;) but with some things that correlate with wealth.
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.
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.
Money buys access to tutors and training materials. It buys access to free time for practicing for your SAT. It also buys opportunity to repeatedly retake the SAT until you get a grade you like.
"Does test preparation help improve student performance on the SAT and ACT?
For students that have taken the test before and would like to boost their scores, coaching
seems to help, but by a rather small amount. After controlling for group differences, the
average coaching boost on the math section of the SAT is 14 to 15 points. The boost is
smaller on the verbal section of the test, just 6 to 8 points. The combined effect of
coaching on the SAT for the NELS sample is about 20 points."
So in fact, it is more likely that people from wealthy backgrounds are able to better utilize their intelligence, and thus retain their wealth and status, whereas people from poor backgrounds are at a disadvantage when it comes to escaping their position in life.
Did you read more than half of one sentence that I wrote? The poor are at a disadvantage when it comes to escaping their position in life; if you need this spelled out for you, the poor are disadvantaged when it comes to making decisions about saving money that could help them improve their financial situation. Wealthy people are better able to make rational decisions about their money, which helps in retaining wealth.
Maybe you should actually read the article I linked to, if it would help you understand what I wrote.
Maybe they aren't as dumb - at least in the area that made them rich - as it seems. I can imagine someone bing smart in the university hall and dumb on the street, or vice versa.
Aren't intelligence and wealth correlated with each other, and both are correlated with SAT and IQ tests? I thought the explanation for the mysterious "g-factor" in intelligence that IQ is supposed to measure isn't that it exists in and of itself, but that a number of measurable outcomes (income, wealth, test scores, GPA, job prestige, etc.) are all positively correlated, and then that correlation is called g.
We need to define some terms. Education != intelligence. The IQ tests are silly and heavily judged as nonsense. These tests are focused on math mostly, but math alone is hardly the only area that matters. However, in this context, math matters, because in many ways it is correlated to programming.
I'd guess that there exists a causal relationship between "intelligence" as measured by standardized tests and the sum of dollars poured into someones education.