You got it right, or at least right in my eyes, and thats whats important. Muu was it? That mummy guy split off into two beings, and split his chakra in half as well. One of them got sealed but the other is still there. This can be true in Madara's case aswell, remember Itachi said that Madara is nothing compared to his former self. This would explain what he meant, Madara split himself in two and one of them died. Probably fight the first at the valley of the end, in order to get some DNA to do his voodo.
If you are thinking it is too random for one splitite to be next to another spiltite, my I remind you that Kabuto is the one who summoned those two near each other.
I can't really bring myself to believe in such an easy explanation, and I don't think that Madara knows how to do the split. The reason why Muu summoned Madara is simply because he is the only one left that isn't in combat or sealed, only a few of the 7 Swordsmen left.
Manga/Anime I read/have read/tried to read:
Full Metal Alchemist
Dragon Ball(Didn't like)
One Piece(Didn't like)
Katakayo Hitman Reborn(Didn't like)
Samurai Champloo(Didn't like)