I've worked with a vollie BLS service. And with full time ALS private amb. serv. which within the city limits worked hand and hand with the ALS Fire/Rescue, and if in the county had a BLS Fire/Rescue respond also. I later got on with the City Fire/Rescue as a Paramedic and a FF II.
I know it sounds complicated but I'll try and simplify it. When I was with the private amb. service and we had a call in the city, both us and the FD responded with the FD Medic in charge and we assisted and did all the transport.
If the call was in the county we responded along with the "District" BLS Fire/Rescue. Our Medic was in charge with the District assisting. And we still did all the transport.
Eventually I moved up (some may not agree) but I got on the City FD full time as a FF II. For a couple of years before that I belonged to the city's version of a Fire/Rescue Voluntary. (I kept busy). Once I got on I only had to respond to calls in the city, which was far less than covering the whole county.
But all in all, I've had experience in who's who, and who's what. I've seen where Medics didn't want anything to do with the fire service, and firefighters who felt the same way with EMS other than Rescue. Eventually the City FD made it mandatory that all new recruits must become Paramedics. That reduced the number of applicants greatly.
So I really can't see an EMS Service heading a Fire based service. You have to take into consideration that Fire Depts. have been around and have been established for many more years than EMS services. If I remember right, Benjamin Franklin was the first Fire Chief in the US and established the first Fire Dept in or around 1787. So for help, the first thing that comes to mind is the Fire Dept., or at least (911).
Sorry, so long, didn't mean to get into a history lesson.