I think the idea is that cats are already very clean, but even more so when wearing pattens.

Wikipedia says:
Pattens are protective overshoes that were worn in Europe from the Middle Ages until the early 20th century. Pattens were worn outdoors over a normal shoe, had a wooden or later wood and metal sole, and were held in place by leather or cloth bands. Pattens functioned to elevate the foot above the mud and dirt (including human effluent and animal dung) of the street, in a period when road and urban paving was minimal.