If no ticket was issued does the insurance company still pay in the state of Texas?

so a couple days ago i "bumped" a 99 ford ranger with my 86 bmw at a stop light. i barely hit him, and the guy never stopped, he just kept going. when i get home 4 cops are at my house saying i fled the scene of an accident. when i explained it to the officer, he said he wrote it up as an accident and did not give me a ticket. the owner of the truck calls me saying i bent his trailer hitch on his ford ranger (aka indestructible) and saying i need to pay him 350 bucks to replace it. i heard that if no ticket was administered then the insurance company will not pay in the state of texas because we are a no fault state. i hope i made this clear.