If payment is demanded upon completion of services, do you doubt that the nurses could have held this gypsy until the police arrived?
I don't know that the police could have done much, except scare the absolute hell out of her, which their mere presence would have done. Cops to gypsies are like crosses to a vampire.
By doing so they would expose themselves to a tort action for false imprisonment --- not too smart and I wouldn't recommend.
Holding a shoplifter when you have physical evidence that they left the store without paying is another matter, because then its clear that the criminal had no intention of paying for the goods, the Corpus delecti of a crime is present, so the imprisonment is legal under notions of citizen arrest.
In the doctor's office example, however, MOST PEOPLE either pay by insurance or by check after invoice by mail, notwithstanding what any sign says in the doctor's office. So it follows that someone who leaves the office without paying is not demoinstrating clear corpus delecti of a crime. Therefore to hold them is, arguably, a false imprisonment,