I've done google searches for all of the videos, and found the inside covers of a few more videos. The inside cover for Rock Music with the Muppets says that Dr. Teeth has his name because he's never had a cavity, while the inside cover for The Kermit and Piggy Story says that Miss Piggy's first name is "Miss" while Kermit's middle name is "the". Gee, it seems a lot of these facts involve character names (Children's Songs and Stories mentions Scooter never riding a scooter).
And of the images I've found in recent memory, most of them begin with "Few people know it, but....", but I saw that in the inside cover for Rock Music, it starts with "Did you know....?"
And do all of the inside cover facts concern the hosts of the videos? Children's Songs and Stories and Country Music both concern the hosts, as opposed to the theme of the videos (Children's Songs and Stories very well could have had a fact about Robin). I remember that the inside cover fact for Muppet Weird Stuff has something to do with Gonzo and Camilla, and I remember the inside cover for either The Muppet Revue or Muppet Moments has a fact about Fozzie, maybe both Kermit and Fozzie.
I also find it interesting how although Beaker is the co-host of Rock Music with the Muppets, he's not pictured on the cover, his hosting duty is not mentioned on the back cover, and he's not mentioned in the inside fact (I didn't mention the lack of a back cover picture because I assume none of the back covers have pictures representing the linking footage). At least the coming attractions for the collection includes a clip with Dr. Teeth and Beaker from the linking footage.