Tutorial The Old World Lizardmen Army PDF is out and free

Yes, this is why extrapolating their two sentence responses to single sentence questions and applying it to other use cases in their FAQs is always bad. They have a tendency to over explain something or provide justification that isn't needed. They didn't have to say ANYTHING beyond "Yes, these wizards can still cast". But GW has a tendency to develop answer diarrheas and say things without understanding second order effects.

They wrote the rules with a bunch of issues the first time. Why do we think they will get everything correct and have no errors the second?

Its always best to take their FAQ answers in isolation. That was a questing about wizards and armour. So the answer is ONLY about that, because that was all the person answering the question was thinking about. They weren't thinking about other characters upgrading to magic armour.