This is a misapplication of Occam's Razor. If a study discovers a correlation between two variables, the Razor does not take the side of either causal direction

This is a misapplication of Occam's Razor. If a study discovers a correlation between two variables, the Razor does not take the side of either causal direction. In this case, the "simplest" explanation as far as the Razor is concerned is not that doctor and patient's gender influences outcomes, and not that probability of some outcome influences the gender of the chosen doctor. I believe (somebody please correct me if I'm wrong) the side the Razor takes is that there is no direct causal relationship at all, which is why the burden of proof is traditionally on the experimenter to demonstrate that such a relationship does exist.