Socioeconomic status (SES) _is_ primarily your family's money. Where it comes from might easily include your family's genetics, e.g. genetics for intelligence. The parent's point, I think, was that controlling for SES in studies of the effect of intelligence on outcomes is likely to be a mistake, because SES itself will be caused by parental intelligence, which correlates with own intelligence via genetic (and other) pathways.
I'm very tired of people demanding that I believe obvious nonsense like this claim that differences in skill don't exist or that differences in skill don't affect material outcomes. I get that you don't like meritocracy, but I'm not going to accept claims that it's some kind of myth. Hard work and talent leads to success.
"over 60 percent of the Forbes richest 400 Americans grew up in substantial privilege" (wikipedia) and add in race and gender rigging of the system and IQ is a factor among others.
Wealth can only accumulate exponentially, and there are big limitations for the "growth" factor. You have to build on the wealth of your parents. This makes it substantially easier for those with richer parents!