The FAA text is annoyingly ambiguous. It refers to warning messages but without any indication of whether the crew experienced any actual control issues. One has to assume without an explicit statement that they did not, but it is remiss of them to issue a statement that "begs the question" in this way.
It is perfectly plausible that, with the loss of a suitable, synchronising time reference, the warning system became unable to function correctly and began to issue frequent and spurious warning messages.
Not a happy situation, but one that is more credible than inertially referenced control systems that not only need a GPS signal, but also malfunction without it.