Based on my experience of living in Mississippi: rural towns do not have swat teams(or a police force besides the county sheriff's office and maybe Highway Patrol if they are nearby), the suburbs also rarely have a swat team however every local police force or sheriff's office will have some "sharing" agreement with whatever the closest city is that allows them request swat if a situation requires it.
As for "nothing happens there" part, domestic violence and it's ability to turn into a hostage situation is usually why a swat team is used and is sadly a common issue; dumb bomb threat pranks to get school closed also appears to be an efficient way to get black trucks to show up in the middle of nowhere.
It's also worth mentioning when comparing US police to other countries that gun ownership should be a factor. Hard to compare what the appropriate fear level should be if the number of firearms encountered during day to day stops differ by magnitudes. Even in rural state like Mississippi that has very liberal gun carry laws, police still seized at least 4500 guns last year; the number of guns encountered in homes/cars/concealed carry that didn't warrant seizure would have a couple of extra zeros if it was tracked.