I have to admit that I do sometimes put my bag on the floor, usually either at home or a carpeted floor. But definitely not in any bathroom floor, let alone a public one! I've never tried putting my bag around a toilet paper dispenser. So thanks for that idea!
I don't freak as much about the floor at home, but still...
If there is no hanger, I try to hang the strap on the corner of the bathroom door stall. This would only work if your straps are flat. And I have also had occassions where I need to just hang the bag from my neck. Haha.. I rarely carry satchels but that might be even harder to find a place to hang.