Pretty much.Its just than Naruto fanboys want him to have the Rinnegan ,that's it.
But I still wonder how Nagato managed to have such a good control over the Rinnegan... maybe the Uzumaki Clan really came from the sage, but through natural means and not with the Creation jutsu.
Whatever, the Sage is not Uzumaki. If the Sage is ancestor of Uzumaki then that doesn't mean that he is Uzumaki, because if that were the case, the Sage is Uchiha too, and the Sage is Senju, and he is all clans he inherited chakra XD.