It still doesn't make sense.

Fire/emergency stations are placed so they can get quickly anywhere in their assigned area. If they're at another call when a real fire starts, it's not statiscally probable to be closer than if they were at the base station. They could be delayed even more by the traffic jam caused by the car accident they're responding to.

So better send one of the vans to heart attacks and car accidents and keep the fire truck at the base stations for fires only.

You definitely seem to have a lot more background in the details and nuances of these systems than I do, sounds like you've got it figured out!