Total BS. My U.S. passport was worn and was set to expire in a few months, so I decided to renew it before traveling back to Thailand. I currently have a valid Thailand DTV visa that still has about four years remaining on it.
I contacted the Thai Consulate in Los Angeles before traveling because I wanted to make sure everything would be fine with my new passport. They told me that because renewing my passport gave me a new passport number, issue date, and expiration date, they cannot update or transfer my existing DTV visa to the new passport.
They said I now have to cancel the current visa and completely reapply for another DTV visa if I want to use it with my renewed passport.
So I am posting this as a warning for anyone else with a Thailand DTV visa: do not assume you can renew your passport and just travel with the new one without checking first. I am glad I contacted them before flying to Bangkok, because otherwise I could have shown up thinking everything was fine.
Unfortunately, I now have to reapply and spend more money after only having this visa for about a year.