Man will you be surprised in 3-5 years.
Just look at voice recognition's progress within the last two years alone. It had reached a plateau of about 80% accuracy, even when speaking slowly, clearly, and without regional accent. Now? I can mutter drunkenly and it'll get it more often than not. I can say very local business words like Phydeaux (upscale pet store) and get the spelling right!
It's called machine learning. The more experience/scenarios etc these self driving cars get, the better they'll be.
I'd say I'm as confident as you (but in the opposite direction) that within 10 years computers will out-drive humans in all scenarios. It won't even be close. 360 degree sub-millisecond informational input versus our meatbag eyes and reflexes??