Many of the hospitals in Boston have surgeons so specialized that they're literally the only surgeon in the US that does their particular type of surgery.

For appendix removal, and trauma surgery, sure, your statement is correct. For brain surgery your statement is a bit ridiculous.

But the problem wasn't finding a surgeon. It was finding an anesthesiologist, who from the story's own description, isn't extra specialised.

Unless that person is on call, it sounds like someone screwed up the schedules by putting an anesthesiologist on a surgery that would take longer than they were still scheduled for.

This wasn't the brain surgeon it was the anesthesiologist.

Oops. Missed that. Sorry