I have decided to bother all the people who like to change the truth about the manga by making false theory. So this thread is to call all the people who have decided to misinterpret chapter 675.
1. What is the Rinnegan?
Rinnegan is the eyes obtain by Rikudo Sennin, whose method of awakening is still unknown. The Rinnegan can also been awakened by mixing chakra from both Ashura and Indra, or chakra from their transmigrants.
Truth: Madara chakra which we speak of when addressing Rinnegan is Indra's chakra
Truth: Hashirama's chakra, which we speak off when addressing is Ashura's chakra.
Truth: The power of Rinnegan that Obito spoke off is Rikudo's chakra = Ashura's + Indra's = Madara's + Hashirama's when they were transmigrant.
False: Saying that Madara chakra is in Rinnegan is false. Rather, one should say that Hagoromo's chakra is in the Rinnegan.
2. Obito and Madara
Obito could not control the Rinnegan power because is body was half Senju and half Uchiha. Basically, Obito does not have Rikudo's body. He has an imperfect half-half body. Similar to Kakashi who did not have Uchiha body, which include the head as well, Obito does not have the same body as Hagoromo or even a copy.
Madara when he was alive did not have Rikudo's body. He was able to mix the two chakra when he was close to death, but he did not actually use the Rinnegan. He couldn't use it because he was weak, and I believe he could not control the power in the same way Obito could not control the power. Otherwise, Madara would be immortal. My evidence is even though Nagato was criple - same as old Madara, he could still control the power of the Rinnegan.
3. Welcome Kabuto.
When Madara was summoned, and when he awakened the Rinnegan as Edo, the first thing he said was about his body. He asked Kabuto how he discovered the secret of his body. Then, Kabuto added that he made him beyond his prime, which means the body Kabuto fashion was better than the one he had when he was alive in his prime - after his fight with Hashirama as well.
Here, we saw that Madara obtained a full fusion of his power and Hashirama's making him able to control EMS, Mokuton, and Rinnegan. Basically, Kabuto gave him what he needed to be close to perfect Rikudo, and this why Kishi made the asspull of reviving Madara with Hashirama's clone body fused with him - which did not make any sense.
So again, the reason Madara is able to control Rinnegan, this time, is because he has a body that is almost the same as that of Rikudo/Hagoromo.
4. Nagato and the Uzumaki
Everyone knows all the theories about the Uzumaki. Most fanboy like to always discard these theory and look for other explanation because they know Naruto is Uzumaki. The truth is that the Uzumaki have exactly Rikudo's bloodline, and this has been shown in many ways.
They are the one who inherited Rikudo's sealing Jutsus. They are the one who can control the Bijus and withstand all kind of chakra. Only ignorant people would not know how Uchiha Sasuke praise Naruto at controlling the evil Kyuubi chakra, and the quantity of chakra naruto can control.
The Uzumaki have strong chakra, strong sensing, strong healing, etc. The only one who has control two Rinnegan without implanting Hashirama's cell is uzumaki Nagato.
This speaks for itself. Uzumaki's have same bloodline as Rikudo Sennin, and the only explanation is that they are either from Rikudo's brother or from a mixing of Uchiha and Senju.
This also say that some rare uzumaki can awaken Rinnegan, and I am pretty sure this fact was part of why they were killed.
While it wasn't cannon, in the movie Lost Tower, there was a girl from a whirpool village who had a watered Rinnegan. All these were hint from Kishi.
Obito cannot control Rinnegan, because his body and mind are not fitted for the power of Rinnegan. This is the same for anyone who is not geniune Uzumaki or does not have both Indra and Ashura power, or simply Rikudo's bloodline. This sound Naruto's Rinnegan which will be actually the Rinnegan to its maximum power - see the symbol of Rinnegan behind Naruto is not a decoration. This also sound bad news for the Sasuketards as it means Sasuke cannot tap into the full power of Rinnegan, and I am pretty sure this is why Kishi kept tomoe on his eye.