Your taxes are already paying for the fire department.
In New York, most Ambulance service is provided by the Fire Department. Billing for Ambulance service is still standard practice. How is this any different?
Why do you pay taxes in NYC if they make you pay for everything again? Would you pay the AAA if they charged you every time you used a tow truck?
If the Fire Department isn't getting enough money, I'd prefer this to them increasing my taxes.