Interesting. In many (most?) US cities firefighters are responding a variety of calls, most commonly more serious car accidents. They also typically hold a number of certifications. Fire calls are uncommon. It makes the most sense from a utilization aspect IMO.
And even when a fire truck responds to a house fire (for example), they may still potentially need to treat and/or evacuate people who have been injured in the fire. Cross-training firefighters so that they can do both makes sense.