It's more common then you think. Some campground have camera pointed at the rear license plate when enter because of this. One campground in Ronake Rapids in particular told me about their problem as they had a camera pointed at the driver coming in and the plate coming in and going out. I was curios about all the cameras at the entrance.
My Uncle who has been a campground host for 30 years had lots of stories about this type of sneaky thief. Since he stayed up late he would see them drive past the night check in. He'd go out with a check-in envelop and write their license plate info on it. He said they always got paid that way.