Self-driving features are indeed being demonstrated to be safer. The video was talking about the different levels of self-driving so maybe we can agree to discuss it on that spectrum.
Tesla publishes some information [1]. I think the others do too. (Take your requisite grains of salt, I work at Tesla.) The the self-driving features are helping reduce accident rates.
I get being skeptical of cars driving for you. I think we should also be concerned with the bad choices that fully fledged human drivers make, how emotions they don't control (or situations they put themselves in) can exacerbate those choices, and how often those things result in damage, injury or loss of life.