Not necessarily - sometimes leaving it alone is precisely the correct thing to do. Examples I can think of off the top of my head are the aforementioned G-ARPI Trident crash, the Aeroflot A310 where the pilot's son partially disengaged the AP, and the German A310 departure from control over Moscow.
In fact these days automation is incredibly reliable and it should be trusted in most cases. However it relies on the same instrument/sensor readings as pilots do, and as such pilots do need to be trained in recognising when things have gone south and how to remedy such situations.