So, how do I know (and not just suspect) that a particular seller is not selling TI parts?

Well there is no way to verify that the device was manufactured by TI. That itself doesn't let you know as a matter of truth, but that does let you as a smart shopper know that it is likely fake. You can make an inference since (A) you are buying on a website that is known for providing a means for counterfeit goods from China, and (B) the seller is located in China and has no info that reliably identifies it as a seller of genuine parts.