Board Thread:Naruto Discussions/@comment-5054236-20150717003436/@comment-734582-20151208112804

I think it's fairly clear that Rinnegan is a genetic ability (the definition of a Kekkei Genkai anyway) and not something you just achieve because you have some chakra. Chakra may activate the genetic ability (how Sharingan/Mangekou is achieved), but that's not the same. By what we know of KKG, Hagoromo could give Naruto and Sasuke his full power and only Sasuke would achieve Rinnegan because he has the genes for it.

Secondarily, remember that Hagoromo possessed the power of All Creation. He turned a bunch of chakra into nine creatures with individual powers and personalities. If he can do something like that, he most definitely can ensure Sasuke gets a rinnegan and naruto gets SPSM