Hi mm43,
In the journalist story I doubt in particular that the autopilot would stay engaged in the event of a double engine flameout, and even if it did, that it would stay engaged until the airplane stalled.
I think it is more likely that the autopilot/autothrust would disengage, and flight path control would then transfer to the FBW flight control system. One has to know more about the flight control system to say what happens next, but a phugoid longitudinal motion associated with variable bank angles does not seem implausible to me.