Upon close examination, I think you are correct, Gail. The wall is about an inch thick. It may well be a piece of wood with the plywood on the outside and the bath wall on the inside. In any event, the small diameter and shortness of the screws is just apparently inadequate for the weight. Mine are now supported by #8 woodscrews 3/4 inches long.
By the way, I checked the mirror screws this morning and about half of them were loose. Now, any rv going down the road can loosen things up over time but was surprised how quickly these caused a problem because when we bought the rig I spent a full day just making sure everything was ship shape.
Paul