You're the expert, but if I was playing a song in a key with G natural and B, E and A flat, I don't think I'd make extensive use of chords feature natural Bs, Es and As (not to mention those two G sharps).

I wouldn't assume the two songs are identical but for the language. According to the Internet, Pete Seeger backed the original mostly with Am, Em (ha!) and D7, which is a whole other kettle of fish. He did also use the stepwise Am/G/F/E, but only between verses.