Texas has some weird laws regarding showing a driver's license. Under the Penal Code, you do not have to identify yourself unless you are arrested. If you are simply "detained" it's not a crime. See Texas Penal Code 38.02.
But under the Transportation Code, a person is required to display a driver's license "on the demand of a magistrate, court officer, or peace officer" if that person is operating a motor vehicle. And even though it's a "fine only" offense, you can still be arrested like this sweet, dear lady with a bladder infection.