My husband & I have been camping for 40+ years and have NEVER had a problem We travel throughout the country and spend a lot of time in Nat'l Parks. But we have never stayed in Walmart parking lots or Rest Areas except a couple times in a very large Welcome Center. My daughter and her family is on vacation now and are finishing up their travels through 45 states. This summer was Florida, Alabama, Georgia, Mississippi, Louisiana, Arkansas and Missouri In order to count as a state they have visited they spend time in the state touring cities, state and/or national parks, and area sites. They have also never encountered any problems.
I wonder if the feeling of lack of safety is more associated with staying at Walmarts and/or Rest Areas.
The one change that we make is in regards to the children in the family. Due to human trafficing concerns even in the midwest, children are never alone. We always went with the kids to play areas, but sometimes they would ride their bikes alone, they no longer do that.