I think it is has to do with the hospitals they end up in. Blacks and whites concentrate and work in different areas and thus end up in different hospitals. Controlling by hospital or income might have enlightening results.
From the link in post 16 -
The NHAMCS is a multistage national probability sample survey of visits to the EDs and outpatient departments of hospitals, exclusive of federal, military, and Veterans Affairs hospitals in the 50 states and the District of Columbia.