So while I know the car could be tampered with, I'm thinking there would be some physical evidence of that. Unless for some reason Hastings just didn't have the presence of mind to turn off the ignition.
I'm thinking that they got to Hastings with something that would make him panic. Why was he going so fast if no one was following him? I think he was either having some kind of panic attack probably drug induced or he was trying to get out of town or get to someone and thought seconds mattered more than being inconspicuous.
If the car has a smart key with a push button starter that is also controlled by the computer. Remember the CHP officer in a loaner Lexus during the "unintended acceleration" flap? He was pounding the button and the car would not shut off. It requires holding the button down for several seconds - like a PC.
If the PCM wants the ignition on, it is on.