As far as I know all self-driving car programs use some form of machine learning, so they aren't exactly "pre-programmed" in the sense of good old-fashioned AI

As far as I know all self-driving car programs use some form of machine learning, so they aren't exactly "pre-programmed" in the sense of good old-fashioned AI based on strict, pre-determined rules. What exactly do you mean by "deal with driving"? Drive without a single accident, ever? That's obviously impossible in practice. Drive better than humans, who in 2016 killed 37,461 people in the US alone? I don't see how that would be impossible - human drivers have a limited field of view, slow response times (average time to break is ~2.3 seconds), and are frequently distracted, sleepy, drunk, etc.