Also more history on your the world not being Governed by them:
Then why were then they so feared in the "Waking the Beast" quest? If they woke up from there true slumber it is said that the world would change and could bring a end to the Terrestial Avatars due to turning them into beasts. So I would have to disagree on them not having any bearing on the world and yes there were Gods like Promathia, Altana, and Zahak *the god you couldn't remember* but Altana raised the Celestial Avatars to the plains of the God's.
Yes, they are not as strong has her but they did have control and power over the world. Also "The 12" only have influence on the continent of Eorzea not the whole world so they do not sound as powerful as you think they are they sound just and bound as the Elemental Avatars do in 11. Citation: ""The Twelve" are twelve benevolent deities of Eorzea who ruled the continent and its surrounding islands until the arrival of wandering tribes. Impressed by the resilience of the primitive settlers, each of the Twelve mercifully saw fit to ensure their welfare. "

So unless there is nothing other then the continent *which we know there is due to some of the seasonal quest talking of the Far East and the Homeland of the Garlen Empire* it seems to me that they might be Gods but not the True Gods of the whole planet *The Source could be the one True God for all we know*.