EE, in the USA the situation would be handled differently. The federal Health Insurance Portability and Accountability Act, commonly known as "HIPAA", is a health records and information privacy law which would make such contact illegal absent the patient's consent.
If the abused person was a child, it would be a different story. But all adults would be required to sign a HIPAA authorization before the hospital could contact any third party, including the police.
In this case, the whole situation could have been avoided if the lady in question simply asked for the cash before providing the requested extras. I have negotiated extras and usually paid in advance. A couple times I paid afterwards, and the lady did not ask for the cash up front, but this was usually with well regarded agencies that knew me as their regular client. Of course if this guy was not dealing with a reputable agency to begin with, and was being upsold, it's curious to me that the girl would not have demanded cash up front especially if she had 2 goons in her pocket and knew it. The story still does not make sense even though EE has provided a plausible explanation for how the police got contacted.
It's also possible the guy got rough with the girl in addition to stiffing her, and that is why the goons went in. Or maybe he had stiffed them before (in which case the girl should have asked for cash up front). Perhaps he deserved the beating he received. And perhaps he knows he deserved to be beaten, and that is why he has not cooperated with the police.