Fits with the there is always one Lord and one Apprentice. The only way to become a Sith is to defeat one.
Obi-Wan did not fall into the Sith when he defeated Darth maul beacuse of 2 reasons - 1. He was not tempted by the Dark Side and 2. Maul (Like Sidious) fell into the hole and the Sith Spirit was not able to enter Obi-Wan.
Does not explain how Dooku became Tyranus, but I can see Anakin defeating Tyranus and taking his place at Sidious' side.