Liability goes with the owner, not the driver. If you let someone drive your car, you are liable for any damage they do.

Not exactly -- legally speaking people are always primarily responsible for their own actions.

However, basically all insurance in the US extends coverage to people who the owner allows to drive the car.

But if you borrow someones car and you cause damages that go beyond their insurance limits, you can be personally sued for the remainder because you are still liable for your actions as a driver.

There are some exceptions where the owner can also be held liable for damages that someone else does, especially when they do it recklessly (e.g. lending to a drunk driver)