The fly in that ointment is that the course change had been entered into the computer atleast 12 minutes before signing off so that all the pilot had to do was push one button after signing off and the plane then changed course.
Well, suppose, for the sake of argument, the flight crew noticed a problem with the electrical system. Perhaps a small amount of smoke or a glitch in the power supply. So they program the autopilot to take them to the nearest emergency airfield, just in case they need to divert if things get worse, and investigate the problem.
In the middle of this investigation, they have a routine sign-off, because they have not yet determined the nature of the problem or if they have an emergency.
After the routine sign-off, things turn for the worse in a hurry. They execute the pre-programmed turn, but are soon overcome by smoke. Once the pilots are incapacitated, the aircraft continues on its last programmed course until all fuel is consumed and they crash into the middle of the Indian Ocean.