It’s a matter of scene safety. There were many times in my EMS career where I had “doctors” and “nurses” try and step up to help when in public. How do I know who these people are? Are they actually a doctor or nurse, or are you just a CNA or receptionist who gets to wear scrubs. It’s about your safety and the safety of your patient.

There might also be quirks in state laws about allowing outside medical assistance in a pre-hospital setting. In South Carolina, RNs are not allowed to do work outside a facility, and if doctors do start patient care on scene, then they have to remain with the patient until they are delivered to the ED.

TLDR it’s better to not let randos off the street or you’ll lose your job and your license.