Yes, it's already happening. Waymo is currently trialling driverless with passengers in Phoenix, Arizona:
https://waymo.com/apply/
https://www.theguardian.com/cities/video/2019/mar/09/waymo-t...
Initial trials will probably include humans if required to avoid needing laws passed (as I think Waymo is doing), I don't really see that as a huge obstacle, and once the human-supervised models can prove they are safe, it'll be easy enough to change regulations if required.
I imagine Musk has had discussions with a few and felt emboldened to make his statement by that. Of course he constantly exaggerates, the projections of possible profit for owners were not realistic (at least in the next decade), and his timelines are about 2x faster than real life, so I'd be surprised if they have more than a small trial next year for this.