Spill the beans

If the precise number of white and black votes were meant to be kept secret and the jar was not meant to be knocked over, how would it have been known whether someone had received a black vote unless the beans were spilt to reveal the votes?

I guess that the 'referee' did the counting and revealed the result, without saying how many votes were black, which would have revealed how many friends and enemies the applicant had. That's assuming you believe the Greek origin. Do you know of a documented better one?