The manual recommends (as I guessed at) using GPS data to get, at least, ground speed. The only problem with this is that at high altitude there can be a large difference between airspeed and ground speed because of the very high winds that can be encountered. In any case, if the stall warnings are going off then it is perfectly possible to increase the thrust and use the artificial horizon instruments to level the craft and to restore a safe flying attitude. It seems like the pilot did not believe the aircraft was in a stall but in a dive. It is a very fundamental error in any aircraft to believe your senses rather than the instruments. It is very basic training in light aircraft to NOT depend on your senses when recovering from a spin, for example, especially in low visibility situations.
Rosy, every pilot would have had some live training on a stall recovery in some aircraft though maybe not in every aircraft he is expected to fly. It should have been done in a simulator though but it looks like the early simulators did not cover this fully (from Geezer's post), which is very surprising, though the omission seems to have been corrected now. Every pilot should be aware of what to do in a stall though. It does look like a case of insufficient practice; the stall would have put the aircraft into an intermediate mode (alternate law, as opposed to normal law and direct law) between fully automatic and manual modes, as the feeds from the airspeed pitot tubes had become unreliable. I suspect he had too many things to think about - OK if you practice enough but not good if you have to look up what to do! We will probably never know exactly.