So apparently the Obyrith screwed up their own reality and pierced the 4e cosmos with the Seed of Evil. This led to the corruption of Tharizdun, who subsequently (IIRC) pushed the primordials to fight the gods.
There are only twelve obyrith left, and they scheme in the Abyss. Pazuzu is one of them, though most don't realize this. It was he that led to the fall of Asmodeus, and Asmodeus took a shard from the Seed as the ruby for his rod.
The Blood War is Asmodeus's invasion of the Abyss to retrieve the rest of the Seed.
You know, it might just be that the obyrith + tanar'ri were always my favorite fiends, but I like this. This is the kind of variation 4e should have been putting in from the beginning...
I hate it. The part about Pazuzu corrupting Asmodeus I like (though I like to think that it also resulted from him spending way too long in the Abyss-- spending years on end on a plane of one's opposite aligment is likely to REALLY screw with an outsider's mind. I mean, they're completely cut off from the essence of their native plane.)
Most of all, I hate the primordials BS. First of all, they classify both the elementals/protogenoi AND the titans as Primordials. Second, they don't classify the Titans as gods. (The protogenoi fit the profile because they theoretically would be able to survive without worshippers, seeing as they predate worship)