Just think, somebody's naked butt would get wiped on that cloth ten times per day. That's a deal-breaker right there.
Actually naturists have a strict towel policy. (Not unlike hitchhikers.) You always have your towel to sit on. Problem solved just by enforcing a "graphic side down" towel sitting policy.
"Don't try to outweird me, three-eyes. I get stranger things than you free with my breakfast cereal." - Zaphod Beeblebrox in "Hithiker's Guide to the Galaxy"