If you read the paper, it says almost nothing about inheritance–it cites someone who did and suggests that those benefits of several thousand a year could compound over time, but in my reading stops short of saying that is the reason. Mainly it seems to debunk certain hypotheses (single-parents, not-employed, education level).
This is corelational research with very small N in many of the groups–the racial advantage persists but it can easily stem from other factors as well as inheritance advantage, such as racism, bad schools, crime records preventing access to good jobs, credit, loans, etc.
