Rinnegan concretely being originally Madara's is bullshit. Like I said before, there's no way Madara knew Nagato back when those three were just orphans wandering around and then teached by Jiraiya. Either he had some role in teaching Nagato later or he's one of the megalomaniac egoists, who think along the lines of: "I'm the greatest Uchiha ever so all special eyes belong to me."