I believe it comes from being "strange" as a 3 dollar bill (because there are no real 3 dollar bills).....there are, of course, 2 dollar bills.....just sayin, lol.
I always would hear old timers say 3 dollar bill, but have heard 2 dollar bill a lot lately. I think, the 2 dollar bill is just someone saying it wrong in the first place and others (like me) repeating it. I think your right it should be 3 dollar bill....:sign0101: