That vinegar cups case is pretty interesting to think about as a foreshadowing case. The "fake eye is fake info" theory is a one take on the data. I actually came to sort of an opposite hypothesis. I forget where I posted this, probably the spoiler cbox, but it strikes me as particularly odd why all the Black Organization members disagree about obvious appearance facts that you would typically notice first about a person like whether Rum is feminine, manly, or old, yet all of them agree on him having a fake eye, especially when fake eyes are usually pretty subtle. One reason why everyone could be hung up on Rum's prosthetic eye is because it is so obvious and striking that everyone's attention is drawn to it to the exclusion of the rest of his features. Think about what would happen if Rum's prosthetic eye is obviously electronic and kind of creepy, while he dresses otherwise nondescriptly like in hat and bulky trenchcoat that covers him up pretty well? You would be too busy staring at his face instead of the rest of him. If asked what the rest of him looked like, you might not be able to recall clearly. A cyborg-like eye wouldn't be out of character for DC as long as there is a reason for it. We have plenty of eye related gadgets already, like Conan's glasses and Kaitou Kid's monocle. What's to say the Organization couldn't doctor up a fake eye gadget for their number two? And maybe to add the confusion he can pop it out in favor of a subtle glass eye when going out in public. That would be quite the cheat. Rum has a Mad-Eye Moody eye theory...