The Prius is a hybrid. It can move with the electric motor without ever starting the gasoline one.
And yes, that could be done completely by the computer.
Problem is, it can't be done when the battery is physically disconnected from the electric motor. When you turn the Prius off, there's a big honkin' relay that actually cuts the supply from the traction battery to the motor. That relay doesn't get connected until the start button gets pressed with a valid key present, plus about a couple of dozen more checks. For a Prius that's actually shut off to start moving would require a cascade of failures to occur just to even get the battery reconnected to the motor. Then, once that happens, the ECU would have to shift itself out of park, which it's designed not to do unless the brake pedal is depressed. So, again, a couple of failures have to occur simultaneously for that to happen.
A much more likely scenario is that someone gets out of the car and forgets to turn the car off because the engine's already stopped. Not saying it's impossible for what the GP described to happen. It's just about a billion times more likely for the driver to screw it up. Occam's razor and all that.