CONF iture,
The start of the UNRELIABLE SPEED INDIC/ADR CHECK PROC assumes worst case, problem at rotation, this was far from being the worst case. They had a lot of altitude on their side. This was far more manageable than when it happens at rotation. The procedure covers all phases of flight, including the cruise in clean configuration.
Switching off the ADR still is not a top priority, flying the aircraft is. This event went over something like 5-10 minutes, not seconds. I am sure you have been thrown false overspeed or stall warnings in the simulator at altitude, and trained not to blindly follow them, cross check them first.
I am well aware of what the checklist says, and in what order. I put the .... in to indicate a break. All I was demonstrating was the existing procedure for dealing with "unjustified stall & overspend warning" would lead you to turning off the ADR. The tools are in the QRH, so are the symptoms to look out for.
I note you did not realise this until I raised it, which makes me think Airbus is right putting it in the OEB for people who not make this connection with the UNRELIABLE SPEED INDIC/ADR CHECK PROC QRH procedure.