I saw that appearance at The Paley Center for Media a few years ago and I wrote about it on the RHLC thread:
Kermit gives a speech about how animated characters can do anything (as opposed to real people). Then when the time comes to announce the winner, Scooter realizes he can't open the envelope! (You know, cause his hands don't work that way!). Kermit gets all flustered saying, "I just got done saying animated characters like us can do anything!"
They cut quickly to Statler and Waldorf in the audience (I think they wonder why these technical problems weren't fixed earlier!), and then back to the stage where now Jim Henson has replaced Kermit and opens the envelope. Jim briefly sounds like Kermit as speaks so he clears his throat and says, "Sorry, I had a frog in my throat!" Scooter laughs at that (sort of humoring his bad joke, lol) and Jim says, "I haven't done that one yet!"
Unfortunately, Richard didn't appear in that bit, probably they figured no one would know who he was, unlike Jim. Still, it's nice to see Scooter listening to the winner's acceptance speech. It keeps the Muppet magic of the moment.