But if you think about it, if those likely to die or have complications after a surgery are complicated case of patients, it's not as if those people would magically be splitted evenly amongst male and female surgeons
As female surgeon are less frequent, complicated cases will likely be taken care of by a male surgeon, therefore this result.
On the other hand, bias in the choice of the surgeon for complicated cases would indeed have the effect you describe.
If this article causes people to conclude that female surgeons are better than males, and thus causes people in the future to choose female surgeons, then the complicated cases will be over-represented and thus their success ratio will plummet
This suggests to me that they have accounted for that to at least some degree. (I can't read the paper itself so I don't know the details.) At the very least I don't think one can simply dismiss the findings out of hand citing "if you think about it."
Instead of immediately looking for reasons why men are actually better in spite of the study and in spite of knowing little about the subject matter, it might behoove you to not simply assume that your trivial case wasn’t accounted for by people who understand their subject quite well, and read the rest with an open mind.