Typically, life-or-death services (e.g. police/fire) fall under the latter, but I guess rural Tennessee is different.
Funny you should mention that, I was watching "House Hunters" on HGTV not too long ago, and they were searching for a home in Tennessee. They looked at homes both inside and outside the small city where they wanted to live and the agent pointed out that the taxes are much lower in the county than in the city. There are consequences for choices like that. This is a common practice in rural parts of the US. Having lived most of my life in Montana, I was actually surprised when I moved to Western Washington to see publicly owned fire houses in rural areas. Every couple years, the people in the counties opt to renew funding for rural fire protection through taxation.
When I was a kid (more than a few decades ago) in Montana, my family moved outside the city to get a bigger space (land and house). When we did, the only services the county provided were the county Sheriff and county road maintenance. I think they had a little equipment for fighting grass fires, but nothing to deal with structures (the costs for equipment and staffing are very different for the two). The county taxes were quite a bit lower than the city taxes and this was the result. For a lot of people who lived in the county lower taxes was a big part of their decision and they got what they paid for. My parents subscribed to a fire fighting service that served most of our county. (They also subscribed to a trash service because the city provided that only to tax payers as well.) We had stickers on every phone, and I think one on the window by the front door, with the number of the fire service, you called them directly back then. There were people in the county who decided they didn't want the protection and decided not to subscribe, but that was their choice and some of them lost their houses every year. Those that lost their homes one year had the reminder of those who lost their homes the year before, but they still chose not to subscribe.
Oh, and we had a burn barrel for burnable trash as well. The trash service charged by the number of cans you had and with 6 children, we produced a lot of trash. What would burn went into a 55 gal drum with no top on it and we threw in a couple of matches.