So this police officer is big enough and strong enough to arrest the nurse and stuff her into a police car, but her saying, "You can't draw the blood," is powerful enough to stop him? How could she physically stop him if he was determined?
I think the better action would be saying, "Drawing that blood is unreasonable search and seizure and assault. I will make a report and be a witness to those facts."
The officer was described as "going off;" an out of control cop is a shooty cop. If you're going to argue with a cop, it had better be in a court room.
He wanted to make an example of her so no one would stand up in the future. IMO it's blown up in his face.