The computer worked to prevent the aircraft from entering an overspeed condition by pitching up and attempting to recover from the dive even before that dual stick input was an issue. It was intervening 13 seconds into the incident, as the aircraft threatened to exceed safety tolerances. The dual stick input created another issue after that intervention began.

The automation very possibly saved lives here. The overspeed protection is good because had that not happened, there's a real possibility that significant sections of the airplane would have sheared off, or the airplane could have rapidly drifted further out of control as it accelerated quickly through 365 knots indicated. Big, heavy, thrusting things gain airspeed rapidly when you pitch them down 18 degrees at cruise power, and the margin of recoverability is very minimal. There are arguments that humans are unable to prevent some scenarios in that situation because by the time higher-order thinking on decisions has happened, it's too late. See, for example, the surprisingly lengthy duration of time between the incident and setting for idle, which probably should have been among the first things done in response. Brains are slow when things happen fast, and a symphony of alarms and whoops (undoubtedly in progress) does not help.

A Boeing would not have intervened in the situation at all and would have allowed the aircraft to go overspeed, risking serious airframe damage. If you crash dive an airliner at cruising speed, very, very bad things happen. At cruising altitude safety envelopes are very small. The paragraph talking about direct law is, roughly speaking, what would have happened had this been a Boeing aircraft. (This isn't bad, it's just different philosophies of pilot responsibility. I'm not partisan on the difference like some pilots and am willing to acknowledge the benefits of both approaches; this one is an Airbus advantage.)