The story I heard on this is Mr. Blanc would actually chew on a carrot in the studio to get the 'Bugs is chewing on a carrot' sound effect. He would then spit it out so he could deliver his lines. Someone witnessing this must have taken it to mean he was allergic.

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Put me on wheels and I'll turn tricks.

Clever? Nah, I ran out of that years ago. But if you find this, let me know, k?
"The road goes ever on..." ~ Tolkien

In memory of my friend skip...
Go then, there are other worlds than these