I think there is something to be said for both arguments.
For example, you can't buy insurance for your car after it's stolen. You can't buy insurance for your house after it burns down. You can't buy health insurance to cover your injury after you get hurt.
Ah, but the federal government does quite commonly let people buy into flood insurance after their houses have been flooded - if the area is declared a 'disaster area' by the government. I have never been sure why that is permitted; after all, I paid for my flood insurance, and my premiums go up to support those who never paid into the system until AFTER they were flooded, and then they only paid the one year's premiums; I've been paying all along.
There is also a difference between private enterprise and their responsibility to the public and government and their responsibility.
When a private company - say a private fire-fighting company - refuses to provide services, it is clearly well within it's rights to do so if the person in question is not a customer. However, a private company would clearly be a bit on the stupid side if they refused to provide services to a non-subscriber on a cost-plus basis (meaning you agree to pay for the costs of putting out the fire, plus a profit markup, at the time of the fire).
When a government agency - city, county, state, or federal - refuses to provide a service, the question is not such a clear one. Obviously, a governmental agency has no obligation to citizens who live outside its jurisdiction. However, it is very common - in fact normal - for agencies to provide mutual aid on request. For example, a neighboring city might provide fire or police services to assist another city in an emergency; the usual understanding is that one hand washes the other; the city providing the assistance has a right to expect such assistance if it ever needs it as well. In some cases, the cost of such assistance is billed to the government agency requesting assistance, which can offset the costs of providing such assistance.
Governments, no matter the size, were established to provide what are termed 'essential services' to citizens within its jurisdiction. In the past, that has clearly been police, fire, road maintenance and clearing, perhaps sewer and water, and other such services. Unlike private industry, governments are permitted to maintain monopolies on such services, and to claim immunity from many kinds of prosecution such as some sort of civil lawsuits. Governments, unlike private industry, can levy taxes, set zoning laws, seize property, and provide court services such as trying and imprisoning citizens when necessary.
Now we are moving into an era of increased privatization, and government resources being stretched to the limit. Governments are hesitant or unable to provide services outside their mandate; and we have more and more issues of police, fire, and other essential services being turned over to private industry to maintain instead.
I suspect we'll see more of this. I'm not sure if it's a good thing or a bad thing. I sympathize with this family and I'm sure that if I am offered fire protection at a price, I'll be budgeting to pay for it. I don't want to risk the consequences.