My wife is a vet and I hear about this often.
From the vet's perspective, if the owner gives up the puppy then they don't have to put the puppy down. Putting down a puppy is heart-wrenching.
You can't give out free medical care, she regularly gives as many discounts as she's allowed to give away, even some she's not supposed to, especially for cases like that. But in the end, the choice is A: put the puppy down or B: do the procedure for free but then the owner has to give up the animal.
When presented that choice it's obvious you should try and convince the owner not to put the animal down.