I also agree with this. I have, in my fan fic career, done one songfic, which was a series of different stories set to lyrics by Sugar Ray. In my case, there was more story than actual song and the songs used were done to highlight the disfunction that Season 4 of ReBoot (which I'm sure Slackbot can attest was the weirdest thing ever).
I have never liked song fics, as most writers just have a song or have a character singing a song, which is just out of place in shows in which characters do not sing. A simple, "X woke up that morning with a song in his heart and sang it" should surfice.
EDIT - My bad: I did have a songfic like chapter in a story of mine, which had a character tell his version of events, starting with him waking up with a song (several) in his heart. But again, in my defense, there was more story than song and at least for the first song, he was using his own lyrics. Said story was a comedy, so it was done in a comedic fashion. Back to original thought -
For a group like the Muppets, who sing and dance and everything under the sun, again there's no need to have the lyrics. I have to assume that anyone who can access this site and thus said story, can also access the Internet and thus the various song lyric websites or YouTube. As I've done with stories that feature Muppet covers, I just post the YouTube link and you're welcomed to check it out or not.