You are correct sir. Air Ambulance (apples) vs Air Rescue (Pears). Risk acceptable for an Air Ambulance flight is no different than that for any air taxi (FAR Pt. 135) flight in the U.S. We're not first responders, just rapid transport for critical care patients.
No first responders?
The video posted from Germany shows a first responder.
Even in the more dense populated Germany, there are areas, where an ambulance just takes to long to arrive.
For heart attack, stroke and some other medical emergencies (bleeding / accidents) time is critical for either survival or good recovery chances.
I.e. stroke, fast medication and transport in a stroke unit, chance of total recovery within weeks is great.
With time wasted, the patient might loose speech and control of limbs for a long time or not even get full control back.
Law is, that for SAR, medical emergencies, police and armed forces you don't have to stick to some of the rules ;-)