Can a few random interaction with cockpit controls result in a crash?
There's a real-life example that seems very similar: Aeroflot 593. The pilots let two children sit in the cockpit while the aircraft was on autopilot. One of the children pushed the control column for 30 seconds, which disengaged the autopilot and started a steep turn. The pilots tried to recover but the aircraft stalled and crashed, killing everyone on board.