As I see it, the Airbus arithmetical addition of inputs allows an instant, instinctive rescue input to be made even if one does not press the take-over button - to flare the aircraft for example. This is the equivalent of feeling the yoke being pulled back by PM, or having the clutch and brake applied by your driving instructor in a dual control car.
Once when first taxiing an A330, I went off the line at a confusing and poorly lit intersection, at night in an unfamiliar US airport. The TRE slammed on the brakes, which was very dramatic, and it shook up the passengers and crew. Had he simply used his tiller to pull the aircraft back on line, and said to me "I have control" or "no, over here", that would have been that, and no drama, (but the 'Dual input' call might have sounded).
The Airbus 'dual input' callout should not be feared, but is a cue for subsequent discussion.