The question is "in a given medical speciality -- internal medicine in this study --, are patient's outcomes related to the admitting physician sex?", not if women make better doctors than females. As such, your point about the best doctors not being in internal medicine is pretty a non sequitur.
Basically, I see two potential biais that could explain at least part of the difference in outcomes :
1. Its is "common knowledge" that male doctors tend to refuse admissions more often than females. (I am not aware of any hard data to prove this point) It could be that the patients that they do admit are somewhat sicker that those they let go directly home. That could explain both higher mortality and re-admission rates.
2. It is again, "common knowledge" (again, I'm not aware of any study) that women write better discharge summaries, including all co-morbid conditions. When coded in a database, those patients will appear sicker than similar ones treated by male doctors, and this could skew any analyses.
A final confounder is that patients often have many doctors during the stay, both male and female, and the study assigned as "the" doctor the one who billed most for the patient, which may not be the one who had the most impact on outcomes. It is difficult to say how this would advantage any particular sex, however.
If that data is true, then we should see a reversed result in other medical areas. It could be that if you wanted the best result of surgery, pick a male doctor. If you want the best result afterward, pick a female doctor.
For example, they exclude all data from ICU doctors because they're disproportionately men – suppose only the best doctors work in the ICU, by excluding that you're excluding more of the best male doctors than the best of the female doctors resulting in leaving a better population of women in your study.
They correct for illness but not for doctor specialty, perhaps females specialize in things that happen to have lower mortality rates.
... and on and on and on. There are so many variables to possibly correct for that a study like this (especially having skimmed it) is pretty much useless. It would be trivial to do a study like this and get whatever result you wanted. Just stop doing statistical corrections when you get the result you're looking for. P-value doesn't mean anything here because it doesn't capture the ways the study could be wrong.