Boeing warns that the stabilizer system can reach its full downward position if not counteracted by pilot trimming the aircraft and disconnecting the stabilizer trim system.
All manufacturers build planes with anti-stall devices.Airbus goes a step further and actually wont allow the stall(normal law).Boeing just warns and aids the pilot to prevent it.Stick shakers,EFS,PLI,the old stick pushers,autoslat,automatic trimming nose down etc etc....all used to help the pilot not stall.All very useful devices.
Until you get unreliable pitot-static data(incl AoA).Then these devices can work against you.
What can the pilot do?What can the manufacturer do?
The pilot must know when there is a mismatch between reality and perception(training....
airmanship....alertness).The pilot must then follow the QRH memory items and religiously disregard the warnings,disable any stall protection system that affects flight control surfaces( and the only one here is trim) and
fly the plane(really not that difficult).EFS doesnt affect flight control surfaces per se it just makes it harder to pull and easier to push.Shakers are tactile warnings.PLI and the like are visual warnings.In the B737 its just the trim thats now working against your control of the ac.
The manufacturer must install these anti-stall devices for certification but cant,as some wise soul above said,prevent pitot-static errors from occurring.Life isnt like that.Errors occur.
Until they come up with something better than the pitot-static system,all they can do is provide data to the pilots in the FCOM and QRH on how to recover from the situation.Somebody a while back posted a picture of a Fokker 100 center pedestal panel(right next to the pilots) showing circuit breakers for overspeed/shaker.This is a very nice design IMO.Its so nice that perhaps it should be an industry standard(with provision of course that switches be protected by covers that have to be flipped by the pilot before they can be activated.... as shown in the Fokker 100 photo)Even with training and good airmanship,the
need for crews to disable spurious warnings(the loud aural and tactile warnings that add to confusion) is of paramount importance,especially so if the UAS event is of longer duration.The manufacturer can also refrain from burying pertinent data in the AMM and start to include it in the FCOM.