The "driving" is done by neural networks that are trained.

If this is true, it's a perfectly fair reason not to trust driverless cars. If you don't know what your code is doing, your code is untrustworthy. Analysis of the systems and subsystems these sorts of networks create is crucial and necessary, regardless of whether it's in driverless cars, protein docking, or whatever else. The code must be understood.

^...

^{Note: I code for a living. I don't do machine learning. I don't deal with driverless cars in any way. I do however have meaningful opinions on what constitutes good code and what constitutes good science.}