In New Zealand it is the pet owner's responsibility to depose of their pets remains. I can't imagine anyone who would choose to leave it up to a vet. Unless you're talking about animals put down by vets at a pound?
Unfortunately two of my childhood dogs had to be euthanized during old age (they were both older than 12 years old) due to Cushing’s disease which is common to their breed. The decision was not taken lightly by my mother and we kept them alive as long as we could. Until they were too much pain for us to stand. Anyhow with Honey we had her euthanized at the vet and they put her in a special box, which we buried in our family garden. Rosie passed away a few years later and we actually had the vet pay a house call. Which apparently is a decision many people opt for as your pet is in familiar territory surrounded by people that love them.
The article was disheartening I have no idea how that vet actually got to be a vet in the first place. Surely someone would've noticed there was something a little off about them?