the "greenie" should be grounded to the outlet box if it's metal, it merely helps from getting the housing charged up - it's a safety issue and would not have anything to do with your current problem.
Something is diverting current when you don't have the light on. In any case, I would consider undoing the wiring and trying to figure it out. If it is wired up wrong and you've got a shunt somewhere, you could be creating a fire hazard.
This one is interesting, wish i was there.. sounds bizarre.