“There’s no way to know if he used the plate on dozens of vehicles in dozens of states, some at the same time.”

So then he's innocent, case closed.

"There's no way to prove him guilty so he should have to pay!"

I doubt the guy had several different car makes on hand to commit some sort of nationwide parking violation spree with the same plate but different cars in places where it's impossible to even drive between the two places in the time between both timestamps.