"the whole point of self-driving cars is that they can react to unexpected circumstances much more quickly than a human"
This statement isn't really true. Do you think Uber is investing in this because it makes their passengers safer? No, they are pretty much immune to any car crashes with a human driver, the risk and insurance hit is assumed by the driver. They are doing this to save money. They don't have to pay a driver for each trip. The safety aspect is just a perk, but Uber will be pushing this full force as long as the self-driving cars are good enough.
I'm more concerned that Uber will "lose" the video evidence showing what kind of situation it was, and we'll never be able to know if a human would have had ample time to react.