Researchers used tourists and swabs to check the cleanliness of the door handles; they focused on "internal toilet doors", what we call stall doors, given that multiple people use them after "potentially unhygienic activities". Go figure.
Here's the guts (as it were) of the results:
"Worldwide the team detected a variety of bacteria common to fecal contamination which could be transferred by touch from toilet door handles to tourists' homes....contamination rates were highest for Staphylococcus aureus, which can cause a variety of infections from sore throats to meningitis, recorded on 5.5 per cent of the samples."
Theoretically, pathogen spread could be ended by proper hand washing. But I'm not holding my breath. Besides people not washing, or not washing properly, there is the issue of the plume of very fine droplets broadcast for some yards by the flush; it's worse with the new ("green") low water use/high water speed fixtures, and with a toilet with the seat cover still open. But who ever closes the seat cover? Further, most of the same low water use commercial fixtures do not incorporate a seat cover.
Personally, I'm looking forward to an even more interesting flu season.