You're basically right. I wasn't aware of this history, but it's very interesting.
Importantly, the factions were competing Catholic Rites, the Melkite and Alexandrian Rites, with the politics of the Roman empire and the Mohammedan invasion thrown in for good measure.
Not a fun time and place to be, huh? Now if only the modern Muslims would get their act together and realize what year it is, the world might be a pretty nice place for a change.