Originally Posted by Gakure
Let's look at it this way, using marriage and inter marriage principles just like bleach Quincies. The Senjus became 2 parties because one group(the now senjus) inter marry themselves to remain pure whilst the other group (the now Uzumakis) tainted their senju genes by marrying from other clans.
Bunch of incest yo!
But really going with that same idea, seeing as how close the Uzumaki and Senju clan were; it wouldn't be surprising that the two had numerous "mixed" children.
Hashimara's wife was an Uzumaki (Mito) so it's fair to say all of Hashimara's descendants are of both uzumaki and senju blood.
It isn't far fetched for KYF and others to believe that Naruto might also have senju blood in his veins. The same way Nagato was considering both senju and Uzumaki in the Manga.