Wasn't the pitot-static system effectively completely hosed in the Perpignan case though (the systems must have been very badly compromised)? I must confess I didn't have an opportunity to follow that one closely at the time.
To summarize Perpignan:
Perpignan accident was enabled when two AOA sensors froze at a low angle of attack while at altitude due to water intrusion. Crew later attempted to demonstrate activation of Alpha protect as part of a functional check flight of the aircraft and went well past into a full stall, autotrimming nearly full nose up in the process. Aircraft dropped into Direct Law (no autotrim) and crew was too busy to notice. High power setting plus nearly full nose up trim caused the nose to rise uncontrollably until stall. Did not pull out from the resulting nose down attitude.