I could travel through a rural area with an extremely high per capita crime rate but my chances of encountering ANY person (good or bad) is low. I effectively avoid crime by avoiding people.
If you live somewhere, you are forced to be a part of the community, which subjects you to the per capita rate.
Still not that. P(you’re the victim) = crime count/potential victim count.
Population density may not be the right number for the denominator, but you need something in there.