I live in a small town as well, only 1400 people (only 13,000 in my whole county). I guess different towns and states are different with different rules and laws. I have been to five different vet clinics and been told no by all of them for "insurance" reasons. Others tell me that they are a vet clinic not a school. I finally got some time in at my local clinic only because my parents are friends with the two vets that own it. Point is at least in Kentucky, its not easy. I have been told that shelters are easier than clinics, but don't know. I do know that Banfield will let you do your clinical hours there, but you have to apply.
I live about 45 minutes from Lexington and will probably have to drive there for my clinical hours at Banfield.
Good luck.