Ashling:
The stall warning is based on AoA so even with unreliable airspeed it will activate correctly. So the stall warning was telling them their AoA was too high. That indication was correct even if their airspeed indications weren't. Its also why you always honour a stall warning with unreliable airspeed.
But the Air Caraibes internal "Unreliable Airspeed" incident report (in somewhat similar circumstances to AF 447, though with significant differences, not least the end result) said [in French, mostly]:
"The PF was absolutely convinced that the two STALL alarms were inappropriate. He used his own judgement to discount the [checklist] phrase RESPECT STALL WARNING AND DISREGARD "RISK OF UNDUE STALL WARNING" STATUS MESSAGE IF DISPLAYED ON ECAM.