My experience was

Hey diddle diddle, the cat and the fiddle,
The cow jumped over the moon,
The little dog laughed, to see such sport
And the dish ran away with the spoon.

And I learned this in 1950's Detroit, so it must be correct. If you ask Blessings Barbara and Harpgirl, I'm sure they'll agree with me.

I don't know that I believe most of the political-allegory theories about the origins of so many nursery rhymes. I think there's a good chance that in cases like this one, the allegory was applied to an existing rhyme.
But that's just my guess, and what do I know?
-Joe-