Was the title ever branded? If you took a settlement but kept the car and already had the title, it is likely that it is still considered a clean title by the state.
If it was salvaged, then you can find the inspection information on the TX DMV website. I think it may be somewhat like a home built trailer, where you take it to their inspector to sign-off, but I admit I'm not certain for cars. It may be as simple as an affidavit and a description of the repairs. Hence, the brand remaining as salvage-rebuilt.