There was more that I missed:
The reasons for the disparity are easy to track, said Christopher Avery, a professor of public policy at Harvard’s John F. Kennedy School of Government who has written extensively on college as an agent of social mobility. Students who earn a degree from an elite college, even those with unimpressive grades and test scores, are simply too far ahead of those who don’t, he said.

Even though some elite institutions are using their vast resources to recruit low-income applicants, a majority of their students come from well-off backgrounds. Tier 1 and 2 graduates are about twice as likely to have parents who graduated from college than students who went to Tier 4 institutions. Their children are instructed from a young age not only in academics but also in the social nuances of making contacts and building relationships.

Tier 4 schools have fewer resources for research and opportunities for undergraduates to take advanced courses and find mentors. With graduation rates below 50 percent at many such institutions, there is little chance to create useful social networks.

“What’s disturbing about this research is that it shows that even if you distinguish yourself as a great student at a Tier 4 school, and by some miracle you get into a good grad program, you aren’t likely to wind up with the tools you need to ever catch up to those people who went to a more selective four-year college,” Dr. Avery said. “You want to think that at some point the playing field is level, but the truth is increasingly clear that the answer is it probably never is. By high school, it’s pretty much over.”