This is exactly it. I'm also a volunteer for a small town, in a department that is decently funded. We have had the same two engines since 2009. We just (within the last month) received a new engine. It became extremely difficult to provide the level of service the community expects, and come up with money for a new engine. It's a major struggle.
Also something most folks don't know: about 70% of the firefighters in the US are volunteers. If you're in a big city you'll have 4 paid folks on an engine (maybe 3 and 1 intern) but as soon as you venture out of the city you'll see more engines 100% staffed by volunteers. And if you don't know the difference that's a good thing!
Fire departments run on budgets that would also shock you (how low they are).