Could it be possible, for argument sake, they did shut down the wrong engine - and then re-ignited with a hot start?
i recall the new orleans CFM engine issue. Although that was brought on by hail ingress at low thrust and weather was fine for this event.
if i recall RE: New Orleans, the left engine after some work on the ground was serviceable - but the right engine, which was overheating after the restart, was damaged beyond repair and had melted the internals and had to be replaced before it was flown back as it was sinking in the embankment.
to 200 experienced pilots - is this a possibility?