I see what you're getting at, xcitation. But the BEA report goes on to say:-
"At 2 h 12 min 02, the PF said "I don’t have any more indications", and the PNF said "we have no valid indications". At that moment, the thrust levers were in the IDLE detent and the engines’ N1’s were at 55%. Around fifteen seconds later, the PF made pitch-down inputs. In the following moments, the angle of attack decreased, the speeds became valid again and the stall warning sounded again."
So if the THS responded to the 'nose-up inputs,' why did it not also respond to the nose-down ones, and instead remain at full nose-up?
While the aeroplane (and the pilots) still had more than 10,000 feet of altitude in hand? Allowing plenty of time for the pilots to level out, climb back to height, and continue on their way?