Perhaps you didn't notice this, but immediately after the point in the transcript you refer to, there's an exchange between the pilots where they establish who's in control (see "vas-y tu as les commandes" at 2 h 13 min 46,0). There is no way to be sure, but it seems probable that this exchange was prompted by the dual input warnings.
>They didn't trust the plane with the information it was providing, which is probably why they ignored these warnings.
There is no indication that they ignored the dual input warnings.
Linking the control sticks doesn't magically resolve problems caused by a breakdown in cockpit discipline. If both pilots are going for the controls at the same time, you're going to have problems. The warning system seems to have done its job, insofar as it prompted the pilots to figure out who was in control.