At fault insurer paid to fix my car but is denying diminished value because 'Texas doesn't allow third party DV.' Is that actually true?

Got rear ended on the tollway last month, full stop in traffic, the other driver was clearly at fault and his carrier accepted liability quickly. They paid for the body shop work, about $7,800, and a rental for two weeks. So far so reasonable.

The car is a 2023 model with 19k miles. After repair it has frame straightening on the carfax now. I asked about diminished value and the adjuster told me flatly that "Texas does not allow third party diminished value claims" and that I was welcome to pursue it through my own insurance. My own carrier said diminished value is not a coverage on my collision policy unless I had specifically purchased it, which I didnt.

So now I am stuck. I tried to trade the car at a dealer this weekend and they offered me $4,200 less than the same car without an accident on the carfax. I have it in writing on the trade appraisal. That is a real loss caused by another drivers negligence and his carrier is telling me the law just doesnt let me recover it.

Has anyone actually pursued a DV claim against a third party carrier in Texas? Is the adjuster telling me the truth or is this a brush off? I dont want to spend money on a lawyer just to find out it was a dead end.