I think this might not be true! I looked at the numbers a few years ago, and Uber had a much higher fatality rate per mile driven then human US drivers. Waymo was better; I forget if it was better than human or not. I couldn't find comparable Tesla numbers --- only PR-style numbers that could be based on all sorts of weird definitions --- but I don't get the impression that they're at the head of the pack.
EDIT: The number to beat is around ~15 deaths per billion miles driven, on the road in the US.
https://en.wikipedia.org/wiki/Transportation_safety_in_the_U...