As a first responder they could be charged with negligence. They had a clear duty to treat and transport the patient. The standard is what a ‘reasonable’ paramedic would have done. 

Speaking as a paramedic, they were being lazy. It is much easier to talk the family into giving the patient a ride to the ER than is to transport them. Less paperwork, or in their case no paperwork.

Where I work it does. We transport people with stubbed toes and tooth aches.