One of the reasons why Ottomans don't attack on Byz is Paradox removed picking Byzantium as rival for Ottomans at the game start
Interestingly, Byz starts out rivaling Ottos, but Ottos can't rival back. I don't think I've ever seen that before; usually, even if you couldn't rival them otherwise, a nation declaring you as rival makes you able to rival them as well.
Now that you mention it, I wonder if that was even intended. Has someone seen it in a changelog somewhere?