The cost of putting out this single fire CAN be quantified. It's ridiculous to think it couldn't.
The firemen went on-site and watched a man's house burn down despite him offering to pay "whatever it costs" to put out the fire.
Certainly if they put out the fire and accepted the $75 fee, everyone outside the city fire coverage would likely cancel their fire coverage.
But if the fire department stated simply, "Sir, you didn't opt in for fire covereage so you will be assessed a fee covering the cost of putting out the fire outside of the coverage. is this acceptable?"
The man would say yes, the city would put out the fire, save the dogs, and likely sue the mortgage company for the house to recover the cost.
They let the house burn, risked losing control of the fire, possibly damaged the property (and property values) of the neighbor which DID pay for coverage.
This is a mistake by the fire dept. they were not responsible for responding to his request for putting out the fire: true. but they were responsible for ensuring the safety and protection of the rest of the paying neighborhood.
A moral obligation is a different issue, and something tells me this man has a history with the municipality that came into play during this decision.