You are making a false assumption that the nurses who are sick with colds are the ones who did not get the flu shot.
The flu shot is the least effective of probably all the vaccines. The CDC admits each year that they usually got the wrong strains of the flu anyways, as they are only guessing.
The rules at the hospital should simply be that if you have a cold or are ill, you should wear a mask or stay away from work.

It is unfair to make the nurses who avoid the toxic ineffective vaccine to wear a mask at all times, when that nurse may in fact have a very healthy lifestyle and rarely ever gets sick.
Meanwhile the nurses who get their shots every year may be the ones sneezing and dripping noses all over the place.

I'm not a nurse, but from what I understand it is pretty hard to get away without wearing the mask when you haven't had the shot.
So I'm pretty sure the nurses you saw in your story above were all fully vaccinated with the flu shots.