You let your kids take the chances, I opted not to.
LOL!
You're right. Bad things don't happen in Wyoming.
Not all of the things are reported on national news...
As far as I know, child abductions make the news just about anywhere. They're also reported and tracked in crime statistics. Those make it clear that it's still a rare thing.
I can teach independence to my child in many ways that are safer than turning him or her loose alone.
"Turning him or her loose alone" is exactly what a parent must do, eventually. By the time your child grows up, she'll need to know how to walk down the street without being afraid. When do you plan to teach her that, and how?