The other thing I thought of was that story of the dog's jubilee.
It was many many years ago when the older dogs in the community considered it was time for a jubilee to mark a dog's life. To cut a long story short, the hall was booked and dogs turned up from far and wide. As a general rule of entry, every dog was to present their rectum at the cloakroom until they all left for home. The cloakroom attendant hung each rectum on a hook under their name tag.
During a rather sexy dance, where the fiddle, played at speed by an old Jack Russell by the name of Rastus, burst into flame. Fire rapidly spread and there was a mad rush for the door and the cloakroom, where every dog was grabbing for a rectum. In their haste, many picked up the wrong one.
So, when you see a dog rush up to another and begin sniffing the others rear end, you can be sure that dog was at the jubilee and was one of those unlucky enough to have to have grabbed the wrong rectum. Until his or her dying day, those ringless dogs will continue their search, hoping that one day they will strike it lucky.