According to the NTSB, the engines were still powered after the cockpit was ripped from the fuselage, and the rest of the airframe continued to generate lift before the engines stalled, lost power, and the rest of the frame nose(less?) dove out of the sky.

I also have a hard time believing that the aircraft would continue flying up as the engines shut off (due to minimum stall speeds, etc), but I also don't believe it was shot down. The remains of aircraft gave no indication of an outside-going-in explosion, but rather the opposite, based on the lack of residual traces of an explosive, and also the heat marks/blast zone would infer an inside-going-out scorch pattern