I have determined the cause of the seemingly random behavior of this bug. When a dispenser or dropper is powered, opening a normal chest causes that dropper or dispenser to update as if the normal chest was a trapped chest. In this case, if you open the chest when the dropper is momentarily powered when it is transporting the very last item, it will cause that dispenser to update and thus transport the last item into the chest. This is of course, not intentional and thus unless you knew what was happening, the times when you open that chest when the dispenser is unpowered would not trigger the dropper to transport the last item into the chest which is why a lot of you can not reproduce it and why it appears to be random at first glance. see https://mojang.atlassian.net/browse/MC-10997
MC-846 describes the well known bug where a dispenser will fire when a block near it receives a redstone update. The point of this bug report is that normal chests are not supposed to be causing redstone updates because that's what the trapped chest is supposed to do. It's specific to normal chests since this update does not occur when other non-redstone powered blocks are placed in the area.