False dichotomy If you are treating a patients wound you have to examine it to see what the problem is It may be that the missed some smaller wounds further up on the head, but that is not the point here
About 25-30 years ago, I pestered any number of medical pros, from paramedics to physicians, about this. They were unanimous that trauma care is applied in strict "ABC" fashion. That is, Airway first, then Breathing, then Circulation. Anything else comes after those three, since there's no point in trying to fix anything else if the patient is neither able to breathe nor pumping blood. As one doctor I asked put it, "On the hierarchy of things medically wrong with JFK at that time, the hole in his head was well down on the list." It may seem strange, until you think about it.
BTW, of the medical people I've talked to, they thought that Carrico, would have had the most careful look at the wound since he was first physician on the scene, and was responsible for the initial examination/triage.