I doubt that both engines would have shut down simultaneously from fuel exhaustion. My experience (12,000 hours) has been that engines always burn fuel a little different, even when set in cruise to the same numbers. I can see a situation where one engine sucked air first, then the autopilot tried to maintain heading or track and altitude or speed, which resulted in a large yaw with roll angle followed by a spiral into the water. Not a long smooth glide as some have talked about here.
Yes, on the B-777 the APU will auto start with loss of both AC generators. Yes, the RAT will auto deploy with loss of both AC generators. Auto electrical load shedding occurs with loss of even one engine AC generator.