Sharon B (from Pintangle.com) shared a link to an old embroidery book that is available to download or browse at the Internet Archive site.
I scrolled through the text and came across this part:
This book was written by ME Wilkinson and published in 1912. It makes me wonder if balls made of loose rags were really common enough to have a stitch defined for making them in Western crafting 100+ years ago.
The balls stitched just with this stitch were probably just utilitarian as opposed to the temari made in Japan around the same time. We have been told that temari making as a useful item (rather than a decorative one) began to wane in the advent of rubber balls becoming available in Japan. Vulcanised Rubber was available in the late 1830's in the Western world but possibly not until after the middle 1800's in Japan when its' borders were opened. Or possibly the final nail in temari as a toy wasn't until the 1960's when compressed synthetic rubber balls were developed.
I suppose I will never know the answer for sure, so I'll just keep myself happy with the knowledge that our ancestors all seem to have made ornamental balls for children from rags both in and outside of Japan. Across cultures, distance and time we humans are all the same.