idk many things are unrevealed yetThan answer this:
If Nagato awakened the Rinnegan naturally, that means there are two pairs of Rinnegan out there. If that were the case, why did Obito wait until Nagato's death to retrieve them?
I think it is very clear that there is only 1 pair of Rinnegan currently in existence, which would imply Madara giving Nagato his Rinnegan.
thier is no evidence besides madara saying that he gave rinnegan to nagato that nagato was given any uchicha dna and it was shown that he awakened it and the manga said that when he gained the rinnegan he killed whoever was there which means if madara or obito or anyone gave it to him they would be dead
notice how nagato is an uzumaki and he is able to use the rinnegan so good while the uchicha need senju dna and when they do get it they still can't use it to it's full potential like nagato