Re: <auto> from Greek autos, reflexive pronoun, "self, same" ...
I agree with your interpretation of what the word means, and that autopilot in this case means something capable of automatically piloting, that is, controlling the car to reach a given destination.
However, I disagree with you that this implies it is safe.
I don't think an aircraft autopilot will avoid collisions with other planes in the air, or if the plane is misconfigured, the ground. If the plane sensors are faulty, it'll make the wrong decisions. I don't think commercial aircraft can fly on autopilot without a pilot as backup, and I think there are various situations where the autopilot will automatically disengage putting the human pilot back in control.
This seems to be very similar to the Tesla autopilot, although the scenarios where the plane one does the right thing far outweigh the situations where the Tesla one works. I'd not trust it, and think it's a daft idea, but i'm rather risk averse, and other people may feel differently.
BTW, another interpretation would be to say that it's a pilot for an auto, which is a fairly common abbreviation for a car, being an automobile. It's unlikely that this is the intention though.