The point of the report is that SAT scores are less correlated with socioeconomic status than other metrics used by admissions like GPA, high school reputation, extracurriculars, essay content, etc. They're still correlated. One of the interesting findings of social science research is that a lot of different metrics like IQ (itself a correlation between different subtest performances), GPA, parental income, child's income, parental wealth, child's wealth, college acceptance chance, eventual education level, ability to delay gratification, general health, etc are all correlated - that's the idea behind the g-factor, a measure of general intelligence that highly correlates with wealth & income. But this research shows that among those correlates, SAT scores are actually less correlated with socioeconomic status than the other metrics that admissions committees can use.

This is also why the SAT was adopted by Harvard in 1934. Prior to that, most students attending Harvard came from private New England boarding schools that could only be afforded by the upper class. They saw an opportunity to diversify the student body by testing the general public and admitting those that scored highest. As an added benefit, the SAT was much easier to grade than previous essay-based admissions standards, and so it reduced cost for the University.