All very good points.
Taking a purely cinematic point of view, I think it's intended that Bishop is human. I think it's hard to explain why, but to me it just feels that way. When bishop says "no, I am Bishop's designer", there's no actual reason to think he's lying. I mean if we're talking about camera work, to indicate somebody lying usually features closeups of hands, or a nervous expression, or a general closeup of the face or mouth.
I think if Bishop was lying there, Fincher would have made it obvious, made a big deal of it, wouldn't have left it to the viewer's imagination. Then again perhaps not.