Therefore, it seems to me that the Juubi actually has that eye (and probably has something to do with the Sharingan/Rinnegan lineage/ the So6P/Uchiha legacy).
This fits with what we know about the clans with notable links to the Rikudou (Uchiha/Senju/Uzumaki/Hyuga). Prior to the Uchiha, no ninja clan or ninja power seems to emphasize Yin energies to the extent that the Sharingan does; where is the precedent to the exceptional Spiritual Energies of the Uchiha Clan, even if they received these from the Rikudou? It's not hard to imagine the Rikudou came from a clan similar to the Senju/Uzumaki, and merely had a very powerful body capable of becoming the Juubi Jinchuuriki. However, as no one besides the Rikudou and Uchiha possessed powerful Spiritual Powers (even the Byakugan lacks significant Yin powers, who ever heard of a Byakugan-based Genjutsu?), I would gladly accept the Juubi being the original source of the Rinnegan.
Perhaps, originally, the only Jutsu were sealing techniques, which the Rikudou's clan possessed. Upon defeating the Juubi and sealing it within himself, the Rikudou awakened the Juubi's Rinnegan (granting him power over Creation / life+death, same as the Juubi). Thus, he understood the nature of chakra/the universe, and passed that down as ninjutsu to humanity. Upon separating the power of the Juubi into the nine Bijuu, he also passed the Juubi's spiritual energies/ doujutsu on to his firstborn son, the Elder Brother / Uchiha forefather.