I have a small story, though it can't compare with Once With Ernie. About two years ago, I think, Caroll Spinney came to my local bookstore to sign copies of "The Wisdom of Big Bird", I went there with my first puppet Kiki the Kiwi Bird and Caroll eventually brought Oscar out.
Before this Caroll saw Kiki on my lap and he said, "Ah a puppeteer!"
I blushed and grinned and said "Somewhat." I was excited and humbled for Caroll to notice me with a two foot bird on my lap.
Back to my original story, I couldn't resist so I put Kiki on and Oscar looked at me and Kiki. He said, "There's a bird in the audience."
Kiki being the smary aleck she is, "I'm not a bird! I'm a Kiwi Bird!"
Then Caroll told a story about how he and his wife went to New Zealand and there were kiwi birds everywhere and how big pests they were. (I don't think that reflected back on my puppet.) Then Oscar said, "Good-bye, Kiwi." and that was that.
So my claim to fame is a one minute bit with Oscar the Grouch.