I can't speak for everywhere, I'll admit. Where I live, the owner is responsible, as I have learned firsthand by involvement in several accident scenarios where the vehicle owner was not driving at the time. You must purchase insurance for each vehicle you own, and if you allow another person to drive your vehicle you retain the liability.
I'm sure there are some exceptions e.g. if your vehicle is stolen, or in cases of a clear contract such as a vehicle lease or rental.
Subject to the foregoing, it seems entirely reasonable that if I allow a random stranger to use my car while I'm at work, that is my decision and my responsibility. And I would not do it.
How is the liability with rental or lease cars though? I think that's the legal structure in which the Tesla car pool would operate in. If Tesla would lease out their own cars instead of sell them, they could make a lot of money too, plus lower the bar for a lot of people to drive it.
I'm sure there are some exceptions e.g. if your vehicle is stolen, or in cases of a clear contract such as a vehicle lease or rental.
Subject to the foregoing, it seems entirely reasonable that if I allow a random stranger to use my car while I'm at work, that is my decision and my responsibility. And I would not do it.