Billy's a cylon.
No, really. Think about it. Cylons have a magical kill-shot zone in their abdomen. Galactica!Sharon had it, and Caprica!Six had a rebar go through her abdomen. And Billy was shot in the abdomen.
So, like, TOTALLY, they're all built with this defect. Maybe that's where their hearts are.
Which makes Billy a Cylon.
Otherwise, he'd be alive.