Riight.. And your uber-safe automatic car is able to react if I, the stupid pedestrian (or worse, because I'm faster, biker) cross a road without looking.

No matter how fast you react, if you go at reasonable speeds and I'm the idiot, you're going to hit me (kill is optional). I think that's what your parent poster was trying to say (because that way it is a sensible argument). Whatever you implement in vehicle safety: If I'm able to throw myself in front of the thing in the last moment, hopefully because I'm a moron and not intentionally, then no technology on earth can avoid the accident.

Unless... You want to add mandatory robot bikes and robot shoes...

I'd argue that a self-driving car can take actions that a human drivers would not be capable of performing...

First of all, it will have much quicker reactions - and in accidents, those extra milliseconds do save lives. Secondly, it can take calm reactions where a human would panic. For example, if a parson started stumbling around drunkenly on a highway, with human drivers zooming past at 70mph a deadly accident is guaranteed. With self-driven cars, it's not that unreasonable to assume that they will be able to spot the person some distance away and change lane to shift around him or her. It might cause a slow-down in traffic around that area, but there's a good chance the whole incident can happen without accidents.