I'm with you on the trivia whiz routine. One of my professors remarked that I'd be a force to be reckoned with on Jeopardy...also, there's a musical trivia board game that my brother and I like to play with our parents. It's called "For the Record," and it deals with rock music trivia; one edition covers the '50s, '60s and '70s, and the other covers the '80s and the '90s. Whenever we all play, it gets a little brutal.
It sounds to me as if they were lip-syncing to a musical number or getting ready for a big crowd scene, in which case it really wouldn't matter who held which Muppet.
In Jim Henson: The Works, in the section about TMM, there's a photo of the performers in the pit outside Lew Lord's office, and it looks as if there's been a switching of puppets. Jim has Kermit and Frank has Miss Piggy, of course, but it looks as if Fozzie's been given to Richard and Scooter's been given to Kathy Mullen.
(incidentally, in Fraggle Rock, it looks as if Richard and Kathy's characters have been teamed up a few times as well)