I was as surprised as anyone to see Belew omitted from the new lineup, but reading the other things Fripp said, it makes sense: Fripp clearly (and characteristically) wants this new incarnation to be something unique, and completely different from previous incarnations. (A three-drummer "front line" with guitar/bass/sax "back line"???) Belew's voice and guitar playing are so distinctive, it would be impossible to NOT sound like Belew-era Crim with him in the lineup.
Also, let's not be too quick to rule out the possibility that it was Belew's choice. After all, he was enthusiastic about joining NIN, but then decided it wasn't right for him, and he's got plenty of other irons in the fire.
My bet is that the decision was mutual. Everything I've seen in recent years suggests that Belew and Fripp are good friends and have stayed in touch regularly, and Fripp gave his blessing to the Crimson ProjeKct, so it's hard for me to imagine that either unilaterally dumped the other without having talked it out. I'll bet that when the story comes out, they'll both say that the decision was mutual and based on "musical differences."