Especially seeing as machines based on e.g. control theory (RichardKennaway) behave much more sensibly - they almost never display any urge to screw up the whole world, instead being content to sit there and tweak their needle.

This is a rather bad example -- machines based on control theory can easily display an "urge" to screw up as much of the world as they can touch. Short version: slapping a PID controller onto a system gives it second order dynamics, and those can have a resonant frequency. If the random disturbance has power at the resonant frequency, the system goes into a positive feedback loop and blows up.