"There is a difference between a song that almost entirely about an event, like a battle, and one that contains a reference to it."

DMcG, thanks for that important clarification.

I'm in total agreement that children's rhymes are "much more about them entertaining themselves than about telling a specific story". Although I believe that these rhymes serve other social purposes,
I don't think that children are conscious of those purposes. And I don't believe that children who recite this rhyme even know or care what those references to Michael Jackson, Coca Cola, and bilgaine mean. Children are much more interested in the rhythm of the rhyme than in what the words they are reciting mean.

That said, I do believe that the inclusion of a passing referent can be used to indicate that in its entirety that specific children's rhyme composition does not precede a particular date. It's important that people don't assume that "date" in this context means the date of composition for each of the separate independent rhymes that make up that particular rhyme composition, but rather for that entire rhyme composition.

I believe that part I of the "Down By The Banks Of The Hanky Panky" rhyme [as presented in the first part of the two rhymes I posted} was adapted from the first verse of "May Irwin's Frog Song" {1896}.
And that song may have been an adaptation of an even earlier song that was in African American oral tradition.

See these excerpts from Mudcat posts:

Subject: RE: Lyr Req: a big bullfrog jumped into the lake
From: GUEST
Date: 28 Dec 04 - 06:39 PM

...It originated back around the turn of the (19th-20th) century as "May Irwin's Frog Song," one of several of this massively built entertainer's hits— others included "Lulu" and "Bully of the Town." She had a knack of picking up song material from black sources, so it's not impossible that hers are rewrites of even earlier stuff. Irwin repays study; I only wish she'd recorded so we could hear the voice that tickled thousands in vaudeville days. --Bob Coltman

and

Subject: Lyr Add: MAY IRWIN'S FROG SONG
From: Jim Dixon - PM
Date: 01 Jan 05 - 03:49 PM

This is the song mentioned above, but it probably isn't the song littledaddy1803 wanted.

The sheet music for MAY IRWIN'S FROG SONG may be found at The Library of Congress American Memory Collection. May Irwin (1862-1938) was the performer, not the songwriter

MAY IRWIN'S FROG SONG
Charles E. Trevathan, 1896

1. Away down a-yonder in Yankety Yank,
A bullfrog jumped from bank to bank
'Cause there wasn't nothin' else to do.
He stubbed his toe an' in he fell,
An' de neighbors all say dat he went to well,
'Cause he hadn't nothin' else to do...