When a human being is so out of control it is as if they are being controlled by a muppet. (The implication is that the human has a muppet's hand up his or her ass, controlling his or her every move.)
Man, Doug is whacked out; he's singing nursery rhymes! That's some muppetic irony shit right there!
Having no control of your own but that of a muppet, with its hand up your butt making your every move for you.
There's a muppetic irony to Petey's lack of self-control...I suspect Kermit, what with his brown-stained hand and all.