A 2004 Century Foundation study found that at the most selective universities and colleges, 74 percent of students come from the richest quarter of the population, while just 3 percent come from the bottom quarter. Rich kids can't possibly be 25 times as likely to be smart as poor kids, so wealth and connections must still matter.
This argument is disingenuous. There are a number of reasons why we might expect poorer individuals would do more poorly at University than wealthier students, on average. Human capital accumulation does not begin in college. Cognitive and non-cognitive skill development start at a young age. Conditional on wealth alone, we should expect wealthier students to be better adapted to college. We should further see budget constraints being less impactful.
Furthermore, the Post's statistics are abysmal. In order for us to have zero poor students going to College, all rich students have to be is some tiny epsilon smarter than the smartest poor student. A ratio of three percent to seventy five percent does not have to be generated by a "high income" distribution with a mean twenty-five times higher than that of the "low income" distribution.