Rafiki, your post reminded me of something that another of our cats used to do...
We got Tabitha (the cat) unexpectedly one morning. My dad had driven my mom to work very early one morning. On his way home, it was pouring rain. She was in the middle of the road, doing what, who knows. My dad, the animal lover, immediately scooped her up and brought her home. She looked like a little wet rat. She was a kitten at this time, all black, with bright gold eyes.
She was definetly a different cat. She could be loving at some times, but normally she was quite aloof. She loved the dog. Used to groom the dog once in awhile.
But the strangest thing she used to do was how she "pottied." No litter box for her. When she had to go, she would find an empty sink, climb in, squat directly over the hole, and go. If it was just to pee, it was fine. She had perfect aim, you would never know she had been there. However, she also used this method for number 2. So every so often, you'd go to a sink, and there would be a little present waiting for you. She did all of this with no training.
Sorry for the image!.