I'm in the U.S. and the idea of cleaning the toilet I'd just used in a public bathroom would never occur to me unless I'd left something *on the seat*, in which case I'd use toilet paper to wipe off the damage. Most public toilets don't have cleaning supplies at the ready, and those that do (say, in a gas station or convenience store) it's assumed they are there for the staff to use.
Given a choice between a bathroom stall that had some skidmarks below the water level and one that didn't, I'd choose the latter. But that sort of skidmark can be done away with by an extra flush or two, especially in a high-traffic public restroom with killer water pressure. Heck, even my home toilet is pretty efficient at flushing away most of them.