Sort of. “Reasonable” towing and storage fees are included in the property damage claim, which is why it’s so important to open claim as soon as possible. By opening the claim, you put the onus on the insurance company to get out there and inspect your car, or even have it towed to one of their own facilities without the storage fees until they can inspect it. Wait too long, and you may be on the hook to cover it yourself — your car, your responsibility.