This isn't really true. The vet isn't selling a product (deceased pets) he is hiring a service (the removal of waste/deceased pets). Just like slaughterhouse refuse is not a product, but something one must pay to have hauled away. If deceased pets are going to be rendered, they would be removed by a deadstock company. If they are not going to be rendered, they would be removed by a company which disposes of medical waste.
I don't see why you think a vet would have an obligation to explain this to anyone. One retains ownership by taking the body or purchasing the survices of a crematorium, or relinquishes ownership of the body and it's disposition is no longer the former owner's concern.
As for the story... I do sort of know, since pet food companies do not go around picking up dead pets. So, I know that it is untrue, I just don't know who is responsible for having made it up.
Hmmm, I honestly don't know about all the waste the slaughterhouse disposes of, but I do know the one here sells some of it. About who disposes of what, guess that is another multiple answer question as, with very little internet research, I found this:
"Besides county roads D & D also specializes in the removal of large animals from private property. If you have other dead animals that need to be removed from private property..."
"I live in long beach, CA and just had my cat euthanized and this is the company the vet said does the cremations with other animals. So I figure they also get all the animals that get put to sleep from animal shelters (horrid). anyway the vet told me they cremate the animals and spread the ashes over vineyards and other places so I am trying to find out a bit more about them but this is all I know for now as well as the review below that says they are the ones that get the road kill for the counties."
But, either way, it would still just depend upon the vet's curiosity, but I am sure they get asked what happens to the animals left behind by many, many owners. Yes, they do owe the owner an answer if the question is asked before the animal is left...as I stated before, the answer might make a difference in whether the owner leaves the animal or not.
About the pet food company picking up dead animals, guess you got me there. I read it about 10 yrs ago, so facts are blurry.