Some people swathe the loo seat with paper before sitting on it.Presumably for hygiene reasons, then if any of it falls on the floor when they stand up, they leave it there because it would be unhygienic to pick it up because it might be contaminated by anything that may have dripped on the floor and dried from other people, and they are afraid of touching it.
I was brought up never to make contact with the seat in a public loo, but just hover squat above it. But in my childhood, there was no soft tissue and Bronco would never have stayed on the loo seat. It would just have slipped off.