ME1, reading through this your question about why it would be a "little colored boy" rather than an adult got me thinking. I had previously come across a song called "The Old Music Master" with a similar theme.
Turns out it was written by Hoagy Carmichael and recorded by Paul Whiteman who had a minor hit with it in 1943.

Here are the opening lyrics:

One night long ago by the light of the moon
An old music master sat composing a tune
His spirit was soaring and his heart full of joy
When right out of nowhere stepped
A little colored boy

You gotta jump it, music master
You gotta play that rhythm faster
You're never gonna get it played
On the Happy Cat Hit Parade

These are the lyrics as found on the internet but the recording I have says "On the Lucky Strike Hit Parade"

Now I wonder if this was inspired by the story about Irving Berlin, or perhaps both spring from an idea common at the time.