so this is your theory..interesting but i have another in mind though...rinnigan belong to uchiha and uzumaki combined...... well its a mutation that took place in nagato body as he had senju blood..... my theory though..... madra gave him only sharingan (uchiha dna) which mutated to rinnigan due to presence of senju blood so basically it belongs to SO6P who had both uzumaki and uchia dna.....
i believe that the rinnegan exist ahead of sharingan...the sharingan descended from the byakugan....remember that in the leaf village, the oldest KG is the Byakugan....and eventually they believe that the sharingan descended from that of the Byakugan....and the rinnegan is already the power of the So6P...