Just speculating here but could it be that, in neighborhoods where a black person is more likely to become a doctor, those neighborhoods have a better healthcare system in place? The cities/neighborhoods with higher black poverty probably have less black doctors in general.
To put your idea differently: The study might be showing that places where a greater ratio of Blacks become doctors have better health outcomes.
This was my conclusion as well. Maybe because I (naively) have trouble imagining that white doctors would reliably care less about black babies than white babies. Regardless, it should be simple to test for: just compare the outcome of all medical care administered in hospitals with relatively high amounts of black doctors to those with low amounts of black doctors.
Caring less does not have to be the only reason. I find it very possible that white doctors are less attuned to the small social and even physical differences (higher risk of certain things) for Black patients. For example, there are studies showing that white doctors are less likely to prescribe pain medication to Black women because they think they are overreacting. Part of that could be overt racism. But lack of time spent around Black people could be another culprit. One being individual racism, the other more a result of systemic racism.
There was no doctor race correlation if baby was white. Which means that it is not just general healthcare quality issue.