couldn't these claims belong to the same woman? Are the insurance claims registered under just a name and address, or is the social security number there too? Everyone always asks for that even though it's technically illegal

Maybe that would help show if it's theft or not.
How can you have a claim on an unknown car? Don't they have a VIN recorded for the claim? You should be able to show that she's never been part of the chain of ownership for that car.