You are likely to find the highest suicide rates in less-populated areas because the average of fewer numbers tends to have a greater variance than the average of more numbers. The suicide rate could be the same everywhere and you would still be guaranteed to find the most suicides in rural counties.
If "small numbers" were the dominant effect, we'd expect to see it move around. This year the highest would be somewhere in the Dakotas, next year in NW Oklahoma, etc. If the rankings are stable over time it must be something else.