That wasn't the issue. Of course they wouldn't. The chances of being incapacitated are/were very small but not zero. So having the staff stay free of a flu would be a "good decision" for the doctors. The risk of them catching the flu would be reduced and the risk from taking a flu shot would be zero. There are some bad side effects from flu shots and the doctors seemed to understand that - at least for the case in question.
I'm not defending the nurse's position. I'm just reporting what she said and I believe that she was sincere. As you can see from the news, people to object to being told they have to take a flu shot.