I don't know all the details of this story, and I don't know if all the facts will ever be out there, but I can answer some questions - at least in regards to how this state works. TN could be vastly different.
Volunteer is kind of a misnomer - volunteer means that they are not paid a wage for shift work type stuff. I don't know of a true volunteer dept., everyone I know of pays something, usually about min wage to $10 an hour. This equates into a cost to the tax payer of about $15 an hour once you factor in insurance/tax etc... Most dept's pay for all training and calls.
On most fires many fire dept's charge per hour .1% of the valuation of the truck. So if a truck is worth $500,000 then you would pay $500 an hour for that truck to be there etc... Then you have other costs like foam, air tank refueling, sometimes the power company being called, law enforcement etc...
A 4 hours fire for wildland easily is $20,000. Structure could easily be more because the trucks are used more, and the actual gear on the fire fighters is being used.
In our state we have a LOT of volunteer fire fighters, however to even say that you are a volunteer fire fighter you need to complete 120 hours of training PER YEAR and that won't even allow you to enter a building.
There are a lot of rules regarding entry into a building so I won't go into that part because pets are not worth a fire fighters life.
Now, in this state fire services are set-up different, and it looks like this state needs to look at changing how they deal with fire services.
Many towns around here do not have fire depts so they contract out to another town - this fee is wrapped into the property tax and therefore everyone is covered.
In the unorganized territory we do have a fire tax, but if it is not paid it is treated like any other unpaid tax and the fire is still put out.
If a fire was set intentionally (in this case you could argue it was since it appears to have started from a barrell) the owner would then be summonsed for any number of things - in this state that could be Burning without a permit, burning prohibited materials, time and manner of kindling, etc.... but the fire would have been extinguised with the first call.
From the sounds of it, the contract is what is faulty. I see the logic of what they did, but they need to change it. I do also agree with the argument that it is like car insurance, you can't call after the accident to get it, or with health insurance, you can't wait to get sick to buy it. It's there in case something happens. However, it should not be set-up in that manner.
In our state we have also now gone to county wide mutual aid - which is a very nice feature. In towns where there is no fire dept. they still contract out with a neighboring town or towns to put out the fires, but if the fire gets too big they can then request outside that contract and that is "free" to the requesting agency. Depending on the cause of the fire restitution can still be granted in court.
In many small towns their fire depts are so small they have also created mutual aid agreements and share frequencies. So if house 1 burns in town A when the tone goes out the tone goes out to ALL the mutual aid towns at once, so A, B, C and D might start their response to the scene. Then if they get there and they can cancel C, and D they do, but at least they were already on route, or if they get there and they are like this is HUGE (example here is a gas station fire that caught the building and was threatening more) they can then do a second tone for E, F, and G from the county and they will start their response. In the case of the gas station fire it included help from 10 fire depts in 3 counties!
It is not unusual on our wildfires to have 8-10 fire depts show up either. Sometimes that might be 8-10 fire fighters or 80-100 fire fighters depending on the populations of the area!
I still don't understand in this case why the animals died since the homeowner and others state it took a long time for the fire to move from the barrel to the structure... the homeowner had plenty of time to retrieve the animals.