I can believe it. I rode in a Waymo for the first time a couple days ago and it was incredible. No problems with the rain or bad San Francisco drivers. It was a really smooth ride and I felt extremely safe.
That's just some good old Musk/Tesla propaganda. Waymo has developed a really high resolution lidar + some software magic means rain is no longer an issue for them.
They have a ton of literature at https://waymo.com/research/ and tech talks on YouTube (search talks by Drago Anguelov). They make heavy use of simulators [1] where they simulate weather events and create their own weather maps [2]. It's a very sophisticated stack.