Starhip - the link you shared does match Lighter's post.

I have an album by noted Ozark folk music historian and songwriter Jimmy Driftwood (the album is Music of the Ozarks, produced by National Geographic) and Driftwood swears the song started life as a bootlegging song, as "Run Johnny Run." He writes:

"Alexander Hamilton’s excise tax of 1791--a special whiskey tax--caused an insurrection in western Pennsylvania in 1794. President Washington sent federal troops to put down the riots. Out of this squabble came ”Run, Johnny, Run,” a song about a moonshiner and his trials with the law. During our Civil War, the Northerners sang a version called “Run, Johnny Reb.” Southerners didn’t like the song, but they liked the tune, so they sang it “Run, Nigger, Run." History has changed the lyrics of many a good old tune, but I had rather sing “Run, Johnny, Run”--even though I have been accused of tampering with the song. Here I play the mouth bow, perhaps mankind’s oldest musical instrument. Made of hickory in the form of a regular hunting bow, it’s played like a jew’s harp."

On my quick search of Mudcat, I didn't see his version here so I thought I'd add it here. As sung on that album (though you can find a much more rousing version that I prefer online here to the dirge-like version on the album)

Johnny was down at the moonshine still,
In the bottom of a holler at the foot of the hill.
He woke up ’bout the break of day
And he thought he heard his grandpa say,

Refrain “Run, Johnny, run, the federals will get you
Run, Johnny, run, you better get away.”

Johnny stopped at the top of the hill,
And he saw them federals around his still,
They busted the barrel and the boiler, too,
And started drinking his mountain dew.

Refrain

The feds caught Johnny making a run,
And they took him up to Washington,
Put him to work for the government
Making moonshine for the President.

Refrain

Johnny got rich at the government stills,
And he ran off to his home in the hills.
Now the federals are on his tracks
He still owes a dollar on the whiskey tax.