I could be wrong, but I just don't think people are going to accept that. It's related to the illusion of control that driving provides: everyone thinks they're a safer-than-average driver. So even if self-driving cars are safe enough for everyone else, they're not safe enough for me.
There will, of course, be exceptions, as we've already seen (poor guy).
Why? If they're overall much safer, then that seems like a net win to me—even if their failure modes are not identical to human ones.