Im confused about how Hiashi and Hizashi were separated into the head and branch family. Its my understanding that the Hyuuga clan dates back further than them (the old guy in episode 63 talks about how in the past, their predecessors had used the branch family as sacrifices in order to protect the secrets of the clan.)

You would think that the clan would have been separated for a long time then, and that the two twin brothers, having come from the same parents who are either members of the head or branch, would have the same identification.

Was this ever explained?