That's the part of this story that's not being told. A little over a decade ago, there was a political power grab wherein the fire department took over all emergency calls. Prior to that, SF had EMTs that would respond in ambulances. This has increased the cost of these programs because firefighters often respond in fire engines instead of ambulances and all responders need to be trained as both fire fighters and EMTs. It's a horribly wasteful policy that makes no sense beyond increasing the political power of the fire department.

Source: I had a friend who was an EMT at the time of the switchover who had to leave the city to work in a nearby area because he didn't want to train for and fight fires.