Je ne comprends rien.
In addition to "We have no valid indications", a couple articles I saw say that the last thing one of the pilots said near the end of the sequence was, "Je ne comprends rien" which means "I don't understand anything."
When automation kicks out (essentially fails) because of conditions, at the least what is left should benefit the pilots dealing with the situation and not confuse it further. What I'm saying is, it seems that some of the bells and whistles sounding once auto pilot kicks out, are remnants from earlier development (older systems) which are a residue which need to be reconsidered, not from the point of view of each individual signal, but the over all effect and usefulness at extreme moments.
Can't there be a redesign of support for extreme moments?
As DozyWannabe said, "The fact is that when you have pitot/static failure, all bets are off when it comes to warnings/indications and the crew must concentrate extremely hard to work out what's going on."