No, because the fire department in question had nothing to do with the government that represented these homeowners, just as the fire department of Rockford, IL has nothing to do with Oak Park.
How does that make false the fact that the municipal fire department is run by a city? Government agencies at local and state levels make arrangements like this all the time without somehow ceasing to be run by the relevant government.
How are "libertarians" and the "free market" involved?
They aren't involved, except to the extent that the South Fulton PD made the mistake of offering market-based coverage to residents of surrounding areas when they should have just kept to their own city.
