Where I work we had some asian or middle-eastern folks who would try to use the standard American-style toilet as a squat toilet. I'm not sure of if they stood on the seat and squatted down or if they straddled the bowl and squatted but either way there was frequently shit on and around the seat. The janitorial staff became quite frustrated with it and someone posted a sign explaining that you had to sit on the toilet and not squat over it.
It must be a big issue in Japan, because every public toilet around here has a big sign telling you not to do that, and explaining how to use the toilet properly.