If you have your Medic you can operate separate from an RN. The ER I was doing clinicals in is staffed by several Medics that practiced their full scope. Only time you work under anyone is if you only have your Basic.
One of the hospitals near me has a few Paramedic ER Techs, and apparently there is some friction between the RNs and the medics because the RNs feel the hospital doesnt have adequate nurse staffing as a result. Instead of having an extra Nurse they will have a Paramedic working, but every patient still has an RN assigned to them so the RNs gripe about their patient ratio being increased.
The Paramedics also make a lot less money than the RNs, so the Nurses see it as the hospital trying to do things on the cheap. At that hospital anyway, the RNs are still sort of in charge though, as they are the ones held legally responsible for each patient.