In the gun store Detectives Zoller and Linehan don't say anything about the drivers license used to purchase the shotguns being from Texas. In fact it says on the form for the background check that the buyer resides in Los Angeles, California and it lists his California driver's license number.
In the gun shop, Zoller and Linehan state the form used to purchase the shotguns had the name of an ex-roommate and his Texas driver's license information listed on it. Later the Diane Sawyer character says in a TV report, on the case, that the ex-roommate's California driver's license had been used to obtain the shotguns used in the murders.