Woody freely admitted using tunes from other songs:
Little Darlin' Pal Of Mine became This Land Is Your Land.
Wildwood Flower became Good Reuban James
Redwing became Union Maid...

I wonder which came first, Tiptoe Through The Tulips or Birth Of The Blues. They're almost the same.
...or Five Foot Two and Please Don't Talk About Me (a bit more of a stretch, but the same progression for sure)