As it has already been stated, Tobi is telling lies or half truths, therefore I think that none can be 100% sure about everything.
For example Nagato's Rinnengan. Could it be possible that he gave away such a gift like that? Or he gave it away while making future and long term plans? There are many possibilities here, but I am sure that Kishi will give us the answers we need soon, or at least some flashbacks will reveal everything.
But one thing is for sure, if Nagato awakened his Rinnengan on his own, then it could be due to some long lost link of the Uzumakis and perhaps Nagato is a long, long, long relative of Rikudo Sennin, aka the Sage of Six Paths.
Personally I would love to see this thing being true since it would be a great twist and plot in the whole story.
I like your idea/theory though, I would +rep you if I knew how to.