Shouldn't they put out the fire, then charge the guy the $11,000? Sure the guy tried to cheat the system, but firefighters should still stop the fire because it is a hazard to the neighbourhood, plus the potential for people being trapped inside. A person's life is not worth less than a $75 monthly fee.
I liken this scenario to a hiker getting lost in the wilderness. They call for a rescue chopper. The chopper has to get them since they are in the business of saving lives, but the hiker is billed for the rescue for being a dumb ass.