Jim Erdman shared a photo of a Disston medallion with the Dec. 27, 1887 patent date reversed in the stamp. My theory follows:
I think Jim has found the medallion equivalent of the often-seen "Henry Disston and Snos" stamp that shows up on backsaws from roughly the same period. Obviously the stamping dies are reversed so the stamped image appear normal on the product that gets stamped. When you look at a word like "sons" or the abbreviation for December, "DEC", upside down and/or backwards, it's easy to be confused whether it will look correct when embossed on the product. The letters "DEC" can be flipped top to bottom and they don't change appearance because they are symmetrical. The keystone is symmetrical when flipped left to right.
The left image is the medallion as it appears. The right image is the mirror image that is what the die would have looked like. If you looked at the word "DEC", you'd think the die was cast correctly. Only looking at the numbers would tell you otherwise. The inner and outer parts of the die may have been designed separately, which could be why the wording around the perimeter of the medallion is correct.
With millions of saws being produced each year in the late 19th and early 20th centuries, I don't think we are talking about every medallion coming from one or two stamps. There must have been many stamping dies operating simultaneously at that time. Why one or more dies were allowed to continue producing faulty product logos for an extended period of time is a question we might never answer. The moral of the story is what printer's apprentices were always taught: Mind your p's and q's.