As far as i know, S&W never sang this. (Maybe they're thinking of It Was a Very Good Year?) Is your friend an obsessed Muppet fan?
I think as a kid he definitely was, but unlike me, he doesn't have any record of his memories. No audio, no VHS, no DVD's. And we've all been guilty of creatively remembering something. I'll try to dig up It Was a Very Good Year and see if that's what he was confusing with HTSBCA.
The funny thing is, because he only saw the Muppet Show "live" back in the day, he can watch a DVD with me, and the memories it evokes are so specific for him, he will begin to recall whose house he was at, what was going on in his life. And then, when a UK spot comes on, he snaps out of the past, and says with wonder, "What is this? Is this one of those UK-only bits? I have never seen this!"
He also described in amazing detail the TV special, "The Muppets Go To The Movies", which I had somehow never seen. I ordered a copy online and every skit was just like he'd described... and he'd only seen it the one time.
Anyway, as to his level of obsession, I think in some ways his manifested stronger than mine. (The Muppets can leave your life for a while, but you never really leave the Muppets.) Around the time we were in college, not too long after Jim Henson's death, my friend (his name is John) got very involved in puppeteering.
There was this group called "The Kids on the Block" and their shows were about teaching schoolchildren that people with disabilities were not something to fear or ostracize. John played a character named Mark, who had CP and was in a wheelchair. The miniature wheelchair cost the organization about a thousand bucks to make, and although he said the weight of it was problematic, he really loved that character's spirit.
I attended a few of the shows he did around here, and what I thought was interesting was that they made zero effort to hide the puppeteers. Because their scripts specifically called for the puppets' legs to be seen-- to demonstrate the differences of one character on crutches, Mark in his wheelchair, etc.-- the puppeteer's hands did not go up through the bodies, they came out the backs of the heads, with the puppet feet standing on a table that was waist-high to the puppeteer. Aside from the 'teers all dressing in black clothes, they didn't do anything to obscure them, not even covering their faces.
I remember a few times that my gaze would go up to a puppeteer, watching how they did the voice or some other aspect of performance, but the puppets always drew attention back to themselves. It's an ancient magic. I've seen clips of Jim Henson doing Kermit on Arsenio Hall, and other interviews, just sitting there on the sofa in plain view, with his arm going up inside the Frog... he definitely knew this magic of 'visible invisibility'.
I myself went a different route of artistic expression during college, getting into theatre and becoming an actor, then a director, and now primarily an improv comedian.
Although... my path too began with a puppet. The very first play that I ever auditioned for was a production of "Little Shop of Horrors", simply because I was such a fan of Frank Oz's film version, and though I was not the brilliant teenage puppeteer for that show, who also scratch-built the Pods, I was delighted to win the role of the Voice of the Plant through a combination of natural talent and sheer reckless willpower.
I have since played that role twice more, at two other venues. In fact, two years ago the same director of the 1989 show called me to reprise the role in his swan song at the local high school, before he left for a better job at a private school in another state. I was very proud that in all his years of teaching drama, he had never found anyone else who could take on Audrey II. I was exactly twice as old as I'd been the first time I played it.
John came and saw that show. To do the lip synch for the Plant properly, sometimes you have to cue the puppet and sometimes the puppet has to cue you, so they built an alcove among the Skid Row scenery where I could see the Pods but the audience could not see me. From my place of concealment, I could see John down in front, his right hand floating in air, unconsciously "mouthing" the lyrics along with the Volkswagen-sized puppet onstage.
DN