The point I was trying to make (but didn't really put in the text, must've been tired) is that both claimed to be caliphs and neither was recognized as such by anyone but their own subjects or vassals.
A Caliph title grab would be nice from a gameplay perspective but from a historical one I think you'd have to incorporate some sort of mechanism to actually be recognized as a legitimate caliph or to reinstate the a recognized caliphate (what that would be I have no idea).
The current decision, if simplistic and perhaps too easy, does seem to fit with how the title was used during the game's timeframe.