I can find other potential bias that would explain the difference in outcomes, like for example internal competition. If female and male doctors move different within the profession and compete on different aspects (a common finding in many other professions), the outcome will also reflect that. The result might thus simply be explained that male doctors compete more for medical positions in areas outside of elder care.

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.