The story Al Ruddy (Hogan's Heros, one of the Godfather producers) tells, is that Russo was being handsy with the female extras, etc...., and just being an ass on set, so Caan decided to rough him up a little with the blessing of some of the crew.
Russo did give this tidbit though, that relates to the Godfather fight scene -
"For all the beatings Caan did land on Russo, however, there is one that sticks out as an obviously staged move.
“That one miss when he throws that punch at me and I react… everybody knows [the punch is actually] about six inches away from me,” he recalls. “I asked Francis Ford Coppola at the 25th anniversary, ‘Why didn’t you fix that?’ Because we had cameras on the roof, cameras all over. We had every angle they needed to fix it, but they couldn’t touch it. Once you win an Oscar, you can’t touch that negative.” "
