Well, when you pit "brain surgery" against "babysitter", it seems pretty clear cut. But imagine if you're that anesthesiologist, or one of a half dozen nurses required for the surgery, or whatever, and you've had to ask your parents to pick your kid up from school for the 12th time this semester because you won't be home before bedtime. Kids tend to not understand these kinds of things, parents know that, and they're rightly frustrated when their job unreasonably demands that their kids get short shrift.

That said, this sounds like a hospital procedure/scheduling fuck up. I don't think the anesthesiologist should be blamed at all, she stood up to unreasonable demands just as she should have. The hospital failed the staff and the patient here.