I'm on an iPod right now but tommoorw I can link neji saying that. I'm positive he says it so can I hear yOur speculati
NOTE: THIS NEARLY BASELESS SPECULATION. if you don't like it... ignore it.
So... we know Nagato was an Uzumaki.
At some point in his past, Tobi and/or Madara implanted Madara's Rinnegan into Nagato so he could use his Rinnei Tensei on Madara.
It's not entirely clear how this is accomplished, but it's probably how it happened.
Tobi specifically mentions that Nagato had his Rinnegan, and Madara specifically states that he's surprised that Nagato lived long enough to use the ability.
The ability of the Rinnegan to be transplanted into a non-Uchiha is important because we know of one other pair of Rinnegan that have existed in the manga: The Sage of the 6 paths had the Rinnegan.
While it is said that the older son had the sage's eyes, the eyes of the sage would still have been around after his death, and i doubt people were real anxious to have their eyes ripped out and replaced with a corpses eyes.
If this is true, then that would provide a good explanation of how the Sharingan gave rise to the Byukagan, and why the Hyuuga aren't technically blood related to the Sage, despite the fact that the Uchiha are.