The study you note focuses on income. There's another branch of research that focuses on wealth that shows that wealth is more important than income when it comes to things like college attendance.
See: http://collegepuzzle.stanford.edu/?p=1590
"“The Differential Impact of Wealth vs. Income in the College-Going Process” finds that wealth and income affect the college choice process differently, with wealth consistently being more significant in predicting who enrolls in college, and the type of college they attend – even after controlling for student differences in academic achievement, habitus, social capital, and cultural capital."
More research clearly needs to be done here, but from what I've seen its clear that wealth looks to dominate income.
And don't get me wrong, I'm not saying there aren't other differences. In fact I suspect there are societal and cultural differences that will manifest in one way or another. If you spend a lot of time in Asian households in the US, you'll see they often resemble, culturally, canonical Asian homes more than "US" homes.
And there's data about the success of African immigrants to the US. Who often don't come wealthy (although some are), obviously are Black, but still do well. So there's clearly a culture issue here too, but I don't think we can really tease this apart without more data.