is the economical definition of a service.

The firefighters are free, the police are free, road maintenance, public schooling, and soup kitchens are just a few free services I can think of. Additionally, some companies offer free services beside their paid services. For example, because I'm a student, H&R Block will help me do my taxes at no charge.

Of course, someone still pays for all these. Your taxes, or other customers, typically. But your "free" health care is still paid for as well, just not by you.

And regardless, even if we chose to argue from now until forever about whether nursing provides a service or not, it still does not make her behavior professional or acceptable. Permitted? yes. But that does not mean she is being a "good nurse" when she behaves in such a manner.