The "Muppets, Inc." thing is kinda confusing, though it seems Henson Associates also continued to be in credits after the company became Jim Henson Productions.
I've seen the back covers for some Sesame Street Atari games, which gave copyright credits for both Muppets, Inc. and Henson Associates. Confusing.
It's interesting about the pre-2000 ownership. I thought The Jim Henson Company owned the full rights to the Sesame Street Muppets, with Sesame Workshop getting 50% of merchandise profits and (according to Jerry Juhl in, I believe, his Muppet Central interview) having to approve of the use of any Sesame Street character appearing in additional Henson productions. Back then the copyright credits only listed Muppets Inc. or Jim Henson Productions as the owner of the characters, with the Muppet movies being the only ones to acknowledge Children's Television Workshop regarding the use of characters (and even then, in MTM the company only got a "special thanks" credit).
In the "Ask Jim Lewis" thread I once asked about why there hadn't been many post-1990 Sesame Street cameos in Henson productions, and he said something to the effect of it was easier to do so when Jim Henson was alive. But Kermit did make quite a few appearances on Sesame Street between 1990-2000. Maybe not too many, but considerably plenty compared to the amount of Sesame Street crossovers with other Henson properties in the 1990s. I wonder if there was any difficulty back then when it came to Kermit appearing on the show or in Sesame Street specials.
You know, I think I once saw a 1990 article about the proposed sale of The Jim Henson Company to Disney, and recall Joan Ganz Cooney saying that after the sale CTW would no longer be allowed to call them Muppets. And yet they are still allowed to call them Muppets, but back in 1990-1991 the credits referred to them as "Sesame Street Puppet Characters", even though that sale was never finalized. And I recently noticed that the credits to The Muppets Celebrate Jim Henson give separate copyright credits regarding the Muppets and "Sesame Street Puppet Characters", despite them both belonging to Henson. Though it seems that now whenever Kermit appears in something Sesame Street-related there are usually separate copyright/trademark credits for "Muppet" and "Kermit the Frog" (as opposed to saying "Kermit the Frog, Muppets, and Muppet are trademarks of Muppets Studio").
It's also interesting how Jim Henson intended on selling his company but not the rights to the Sesame Street characters. How could a company own another company but not every property owned by the company it owns? Would Henson have had to form a subsidary allowing Jim Henson to own the Sesame Street Muppets while Disney owned the rest of The Jim Henson Company or what...?