I do not think it talks about whether one exists and the other does not. It talks about affinity with Yin and Yang. Think about how ninjas have an affinity in one of the Five Elements.
The chart show the affinity that the Ninjas have in Yin and Yang. Some have Yin, Some Yang, Some both and some neither.
Because I remember somewhere in the databook it said that the yin/yang thing was just a fragment of their justus. Kind of like how genjustu experts are yin dominant, shadow clone experts are yang dominant, and ones with both are proficient with both.
I thought OP was talking about people who had the kekkai genkai yin-yang release like black rods, gudodamas, inzanagi, and creation of all things type of deal.
I agree. Onmyoudon is a Sage technique that has to be activated and requires Yin-Yang Release.
I'm still unsure of how Hamura or Toneri attained RSM.
Well, I have no knowledge on the movie, but I do know that having only Rikudou Chakra doesn't negate Ninjutsu. But then again, it doesn't matter whether or not they had Onmyoudon because Naruto and Sasuke use Rikudou Chakra.
It mattered against the five kage who almost killed Kinshiki. Hamura got it from the same source as Kaguya, hus mother. Toneri used hamuras power the tenseigan.
Actually Chatte's theory has a case in point. In the long run it might come true if it fits with the context of the manga. That theory focuses mainly on the significance of the Third Eye (If you can bother, feel free to do research on it).
Returning back to my case,
It has being heavily implied multiple times in the manga that Yin + Yang = Rinnegan.
This in a way (Mind me for breaking an iceberg) means that Yin and Yang cannot exist separately and still form a Rinnegan. They must be one and combined to do so.
If Hagoromo gave Naruto and Sasuke his chakra by dividing it into Yin and Yang, then neither of them would have awakened Rinnegan.
The Rinnegan has two properties :-
Yin and Yang in balance.
Yin and Yang are one force.
Creating the Rinnegan.
It's important before you start that Hagoromo's power got divided genetically (Same happened to Kaguya) between Indra (Yin) and Ashura (Yang).
Naruto and Sasuke had the Spirits and chakra of Indra and Ashura (Transmigrants). Hagoromo knew that giving them his Rikudou chakra would throw off the Yin and Yang balance cause Sasuke will become Yin Dominant (Hagoromo + Extra Indra) and Naruto will become Yang Dominant (Hagoromo + Extra Ashura). This is why he divided the Yin and Yang seals between them accordingly to their dominant halves.
Since Sasuke was Yin dominant, he awakened the Rinnegan Eye/Doujutsu but his Yang/RSM became recessive so he did not get the Rinnegan Body Symbol.
In Naruto's case, he was Yang Dominant as such he awakened the Rinnegan RSM/Body symbol and his Yin/Rinnegan Doujutsu became recessive so he did not awaken it.
If Naruto and Sasuke were not Indra and Ashura's transmigrants, they would be literal copies of Hagoromo, with Rinnegan Eyes and Rinnegan Body symbols with both Rinnegan Doujutsu and RSM at it's full potential.
Madara was deluded by Black Zetsu's words, he didn't even know about the Indra and Ashura chakra system (As far as I remember), so it's pretty obvious that he would misinterpret the real powers of Naruto and Sasuke. Plus Madara would have never admitted it openly anyways even if he knew cause of his inflated Ego.
In the end, I would rather follow the context of the manga rather than the words of a deluded man (I mean Madara).
I don't think Hagoromo divided his Rikudou chakra into Yin and Yang. He gave them both the complete portions of his chakra hence they both awakened Rinnegans. This would mean they both have the powers of RSM and Rinnegan. Sasuke's Rinnegan is amplified because he has Hagoromo + Indra (Yin gets dominant) whereas Naruto's RSM is amplified because he has Hagoromo + Ashura (Yang gets dominant).
Naruto couldn't awaken RSM without having the Rikodou Senjutsu chakra, which is different from the chakra Sasuke attained. So obviously they both received different chakras.
But your theory is also not out of possibility. It's somewhat viable if we don't go harsh into the details. It could be possible that both Naruto and Sasuke received the same Rikodou chakra and they merged that chakra with their existing chakras for greater power. For example, Naruto attains RSM by combining his Rikodou chakra with his Ashura chakra. But honestly, that doesn't form Senjutsu chakra by any means unless Hagoromo specifically gave the capability.
But your point about both having Rinnegan and RSM is totally false.
