The argument about "who was flying the plane" is madness.
The FO was pilot flying having 'taken control' off the back of a monitored approach. He intended to disconnect the AP at approx 600ft, but due to the obvious distractions he didn't, or believed that he had.
Either way, the aircraft was flying as he expected it to (except the distinct lack of power). If he was manipulating the controls, or trimming, the AP would have dropped out anyway - but as its flight path was essentially as desired, it doesn't matter.
All pilots know that aircraft don't have to be flown hands on, AP connected or not.