Yes, they were. They got stuck with ice and they disagreed in the air speed sent. Because of this the autopilot was disabled and the flight controls were switched in alternate law 2. The pilot that was flying failed to realise that this meant that his inputs had a much bigger effect compared to normal flight and he panicked and he also failed to relinquish control to the much more experienced pilot (on that model) multiple times. How are the pitot tubes not the root cause?

Malfunctioning pitot tubes do not cause an otherwise fine airplane to depart controlled flight.

The root cause was human factors.

Even then, they still fixed the tubes on all their planes. Seems only right, doesn't it?