Human drivers are very very bad. Being better than humans is a low bar with plenty of room to be bad as well.
Those who work on self driving cars say they have cleared it - but they have an obvious bias. Nobody independent has done a full study of this, so we have no particular reason to believe them, but we also shouldn't completely discount them (when the truth is in their favor everyone with a bias will tell it, and some people are even able to overcome their bias when the truth is against them)