I love this idea that the essence of these poems are in the rhythm, vocalizations, and play and not in the specific words themselves.
When I was small, my parents would tell me a toe-counting rhyme, which I knew as "icky-pee, penny lou". I wanted to learn what the "real" words were and found this page [1]. In the comments there are dozens of variations on this same poem and none use the same phrasing we did.
Oral traditions seem to have a way of distilling information to essences over time vs. bit-wise copies.
[1]: http://www.mamalisa.com/blog/the-origins-of-some-scandinavia...