You know, I think people are too fixated on this approach. Reality is not a Paradox game where the moment you include a discordant factor everything goes completely off-the-rails. Things happen in history for a reason. The emergence of Islam wasn't an accident, it was a result of hundreds upon hundreds of years of history of the Arabian Peninsula. Changing one element in a (at that point) unrelated part of the world doesn't have to butterfly it away (though it can).
Paradox games have far too much predetermination to be considered true alternate history (not that I blame them; it'd take a supercomputer to calculate all the ways history could differ from every seemingly insignificant action). The fact is that any PoD completely changes history. A one second delay means that different babies will be born, different events will happen- perhaps it will result in people meeting or not meeting at a crucial time, etc. The PoDs multiply after the initial PoD- we're not talking about one little change, we're talking about millions, billions, perhaps trillions of changes, which will only increase as time goes on- those genetically different infants will grow up and not necessarily act the same way as those that were born OTL, and they'll definitely marry different people- it's not that Mohammed wouldn't just be born, it's that several centuries of his ancestors wouldn't be born.