I don't think we will ever know what really happened. However, stealing a spare tire and rack in the middle of the night, in a RV park where such activity would likely be noticed (RV parks are high density and usually sites aren't very private) sure isn't a sign of a criminal mastermind. The tire rack would likely have no value, and a spare tire very little though both would have some weight to them. That's a whole lot of work, for little reward. Most tire and wheel thieves target more valuable aluminum wheels on popular vehicles. Twice in my Lifetime I have come out to find my truck on blocks (not in Montana, but back when I lived the corporate life), but the spare remained untouched. A set of 4 tires with expensive wheels have resale value, a single trailer tire spare, not so much.
As for falling off, physics would dictate that if it fell off the back of a moving vehicle, it would not hit the vehicle since the tire and carrier would begin decelerating once it became unattached while the vehicle would maintain it's speed. Furthermore, any sound would be blocked by the trailer and the vehicle and muffled by other road noises. I've had things vibrate loose over the years and disappear into the side of the road abyss.