This topic comes up on the interwebz with surprising frequency, considering how uncommonly it actually happens.
In 15 years I've had two physicians on scene. The first, I was a new-ish paramedic responding to a call in a public place (I don't even remember what the call was for or where exactly it was), and when I got there, someone who happened to be a doctor was trying to make the patient comfortable while they waited for us. He identified himself and told us that if there was anything he could do to help, to please let him know, and then he stepped away. Second one was a serious multi-car MVC with numerous patients in a small, rural town that we responded to with 3 helicopters. When we landed on scene, an anesthesiologist from the nearby small hospital was wearing bloody scrubs just doing whatever he could to help EMS. The ED had sent him there to help when EMS called in telling OLMD that they had several patient who needed airway management. He intubated 2 patients, possibly saving their lives because they were pretty sick. He too, offered us any help he could before simply stepping away and letting us do our thing.
My point is not to rehash war stories, but just to illustrate how on-scene physicians usually work. In the real world, I've never even heard of an on-scene physician making things difficult and refusing to turn over care to EMS. I'm sure it happens occasionally, but it's a truly rare occurrence.