Sorry I am not a vet, but in that situation, I think the best, although unpleasant, option would be to agree to do it. If they refused on ethical grounds, they can't force the owner to manage to condition correctly, so you are likely to end up with an animal suffering, or even dumped, because the owner doesn't have the resources to manage the condition.
It obviously depends on the condition though, and how much suffering it would cause the animal, as well as how much time and effort, the managing of the condition would take.
I am afraid that in these financially and time constrained times euthanasia is often a treatment option. Not something we like, but whilst the condition is manageable if the owner is not prepared to manage it euthanasia can be the best option for the pet.