Ultimately they do have to prove that the DVD's were counterfeit, yes. There are ways to do that without having the actual hard copy of the DVD, however. That does not mean they will be able to. Furthermore, even if the DVD's are only "available" through certain "approved" sellers, they have no right to prevent anyone from reselling the DVD once he owns it.
Your question ultimately will not be able to answered until you say whether or not the DVD really were counterfeit or not, and you lay out -- ideally to an experienced attorney -- all the facts and circumstances.