I've read the thread, and nobody seems to have noted that in the original film version (With Donald Sutherland) the song was about the death wish of the camp dentist.
Dentists , it seems, often have the nickname 'Painless' as was the case here.
Also I remember Bobe Hope as the dentist "Painless Potter" in either "The Paleface" or "Son of Paleface"

Nigel