You are correct. Basic US contract law.
Per Article 2 of the Uniform Commercial Code, the store PDA (not the purchaser) entered into a shipping contract with DSX. The contract was PDA payment for DSX delivery services. Therefore, only PDA has standing in a shipping dispute with PDX, not the purchaser being delivered to.
If the package was lost in transit and never delivered, then the dispute is entirely between PDA and DSX. If the package was delivered damaged or missing items, PDA may need the customer's cooperation so PDA can file the claim with DSX. If the customer does not cooperate, then PDA can't file an accurate/complete claim and the claim will be denied. That's where people get confused. If the customer is in posesdion of the damaged box, they may have to cooperate.
Example, I recently ordered a few items from Accurate Reloading dot com. The package arrived carefully cut opened and re-sealed with a $50 item missing. In order to file a USPS claim, AR requested pics of the box. I sent pics. The USPS then requested I bring the box and ALL contents to a USPS location. I did. The USPS wanted to permanently confiscate the box and ALL of the items in it. I declined to cooperate because the missing item was $50 but I also purchased a $175 set of rare special dies that I had already started using and I did not want to surrender. I was better off taking the $50 loss myself than returning the rare $175 dies and not being able to find them again, or having AR reject my return because the dies were opened and used. Since I declined to cooperate with the claim/investigation, USPS denied the claim and I lost my $50. I kept very good communication with Accurate Reloading during this process, but they would not refund my missing item because I didn't want to return ALL of the items in my order to USPS. I no longer use AR, because I explained this to them but the owner was unreasonable, she initially blamed me and over a week period of back and forth emails and phone calls she never apologized for my troubles as a customer. Other stores like Midway or Brownells would have simply refunded my $50 or sent out another item no questions asked.