"What else than lack of lift => lack of speed can cause falling that bird so fast from the sky? Did they believe that they are in a dive/overspeed situation? "
well, like by many times written above- basicly nothing other than a stall, with high nose up and this sink rate you can exclude a dive. basicly a PPL owner would answer this question.
one thing ist that it was night, possibly IMC and there was turbulence. they probably had not any visual reference to the natural horizon outside and maybe they did not believed the pitch indication on their instruments.
i think the big question we had at the day of the crash WHAT happened is fully answered, it may be of interest to read the thread no1 what kind of speculation there was made. the question WHY it happened will never be answered because the people who know why they pulled until impact will not tell you.