It's possible that your friend heard one of the parodies/adaptations of Mercer's original, and it's Mercer's that he has in mind when he says "the song" is a parody?

Find A Grave The Bowery Boys identifies "Satch" (the way it was pronounced) as:

Hall, Huntz (Henry)    b. August 15, 1919 d. January 30, 1999
Popular motion picture actor of the 1930s to 1990s. Fondly remembered for his role of 'Sach' in a number of East Side Kids and Bowery Boys films.

Iff there's a possible connection to a satirical "Old Cowhand" in the lyric linked in the original post, it would be the Bboys version that was the satire on the Mercer original, perhaps, and this might be the connection remembered by someone(?).

"East Side Kids," "Bowery Boys," and "Dead End Kids" were names applied to this particular gang's series of movies.

If someone really wanted to pursue this, more information might be found searching on the "leader" of the gang, than on other members:

Gorcey, Leo    b. June 3, 1917 d. June 2, 1969
American motion picture actor of the 1930s, 40s, 50s, and 60s. Widely known as the leader of the "Eastside Kids," the "Dead End Kids," and "The Bowery Boys

Other gang members:
Halop, Billy    b. February 11, 1920 d. November 9, 1976
Jordan, Bobby    b. April 1, 1923 d. September 10, 1965
Punsly, Bernard   b. July 11, 1923 d. January 20, 2004

I don't' recall what "stage names" any of the others used in the films.

Vintage Library lists some of their films, but not the few "Out West" ones I recall. I suspect they were fairly late in their run of movies, possibly late 40s or early 50s.

Note that searches for "Bowery Boys" may turn up the real gangs of an earlier era as described by Answers.com: Bowery Boys but I don't' think they did satire. (But there might be songs about them.)

John