If a car that was reported stolen hits your car why would the stolen car's insurance company refuse to pay for damages?

Probably because the owner did not exercise normal precautions and by leaving the keys in the vehicle actually participated in its theft. Call that lawyer who advertises on TV. If he can't get the insurance to pay, he'll get a judgment against the owner.

The owner of a stolen vehicle is not responsible for the actions of the thief that stole their vehicle. If there is no liability on the owner, the insurance company does not owe the claim for property damage to others.