I just read your description of how to make the "tape and paper balls" with newspaper and duct tape, and suddenly I understand something I have wondered about for months! I live very close to a small neighborhood park where people often go with their dogs to play fetch or frisbee. A month or so ago I went there with my dog, and while sniffing around the bushes, she rolled out this little almost-round wad of something that was tightly wrapped in duct tape. It was about the size and shape of a tennis ball. There was a second one just like it on the ground on the other side of the park. My dog carried it around in her mouth for a while, but I was afraid that there was something inside the tape that could be potentially dangerous, so I took it away from her. When I look at the photos of the Tape and Paper balls, that is EXACTLY what it looked like! Perhaps someone in my neighborhood has made them too!
Mystery solved. (and p.s. Apparently my dog loves them too!)