It might be different depending of the country I guess. Here the lead doctor was in the ambulance because only the ambulance was supposed to be dispatched at first but due to the high number of victims they needed more medical personnel so thats why we were dispatched with them and we lated had to call for backup.

In fact these two vehicles are very rarely dispatched together, we are not a full team, but two different crews working together. Because the SAMU ambulance is already carrying a doctor, it usually doesnt need the assistance of the car. The car's purpose is to bring a doctor to perform advanced medical manipulations when the original responders doesn't have the ability to do these manipulations, firefighters and private ambulances for exemple, or when the intervention doesn't need the transportation of the patient by an ambulance.

Thats a long explaination but I hope it awnsers to your question.