Except that you are talking about religious organizations. So you are positing that the Pope is not a True Believer? Osama bin Laden was not a True Believer? The Saudi Royal family are not True Believers? The Iranian Ayatollahs are not True Believers?
Seriously?
There may or may not be a figurehead who is a true believer, but the actual powers that be in major orgs are in that position due to realpolitik. And I'd say that most "religious" orgs that transcend a certain size and scope become more about politics than piety. This is especially true of Muslims, since their messianic figure made their religion explicitly political.