I have listed to several sound samples of SIGNIFYING MONKEY by Willie Dixon at allmusic, and they are definitely NOT the same as Bartholomew's THE MONKEY.

Furthermore, while the traditional SIGNIFYING MONKEY was a recitation, not a song, Willie Dixon's version is definitely a song. Evidently he wrote a tune to go with the traditional words, and as such, he is justified in claiming copyright to the tune. Maybe he altered the words as well.

Here's what I transcribed from the sound samples. (I don't know whether I have the two sections in the right order):

...Said, now, big boy, it's you or me
The elephant looks from the corner of his eyes
Better find someone to fight your side
The lion jumps up and makes a fancy pass
But the elephant knocks him over in the grass
They fought all night and they fought all day
Don't know how the lion, well, he got away.
He come back to the jungle more dead than alive
And that's when the monkey really started his jive
You call yourself the jungle king
You call yourself the jungle king
You call yourself the jungle king
I found out you ain't a doggone thing....

...Well, he waked up his tempo (?) when he jumpin' up an' down
And his foot missed a limb and his head hit the ground
Like a bolt of lightnin' and a streak of heat
The lion was on him with all four feet
But the monkey looks up from the corner of his eyes
Says, now, mister lion, I apologize
The monkey on his back studies up a scheme
He's tryin' to trick that jungle king....