Apparently their pitot tubes froze up because of faulty probes that hadn't been replaced yet
I don't think that can be established as a fact. Faulty is not the right word anyway imo. There were certainly probes ready to go on that
should be at least a bit better in icing conditions, but it is by no means certain that they would not have frozen up as well in the conditions they encountered which could have been anything from very severe...to moderate. We'll never know.