They acted on it. Wikipedia writes: "On 12 August 2009, Airbus issued three mandatory service bulletins, requiring that all A330 and A340 aircraft be fitted with two Goodrich 0851HL pitot tubes and one Thales model C16195BA pitot (or, alternatively, three of the Goodrich pitot tubes); Thales model C16195AA pitot tubes were no longer to be used."
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?