Compulsory liability insurance - this one pays out for damages and injuries to the victim of a collision you caused.
Comprehensive insurance - covers everything even if you are the cause of accident.
>the owners of the Model X file for claims 41 percent more often than average,
What exactly does that mean? Did they cause the accident, or did someone else rear ended their Tesla? This smells like victim blaming.
From what I hear, bumper replacement alone can top $10k on a Model S.
To me, European, statement "AAA claims Tesla owners should pay more" means they want to bump price of compulsory insurance for Tesla owners - insurance that covers damage done to other cars, not the expensive Teslas. No one is stopping you from charging more for voluntary coverage.
Those are rate lines independent of liability.
Thus, while you can carry just liability insurance on your vehicle in most states, it isn't all that common, aside from older, paid-off vehicles, or used clunkers that are cheap enough for people to buy outright without financing.
One thing that is likely is that if minor repairs cost an arm and a leg, Tesla owners will file claims for things that owners of other cars wouldn't file claims for because filing a claim raises your premiums. Probability of filing a claim !== probability of having an accident, but it is what determines how expensive the car is to insure.