Yes, vets have an obligation to relieve suffering - however, this includes providing euthanasia if the treatment is too expensive for the owner.
So sending a suffering animal away without treating it is an offence. Giving the owner two options (PTS or pay for treatment) is not an offence.
In other words, the vet is under an obligation to do something to relieve suffering, but they are not under any obligation to provide the owner's preferred treatment if the owner cannot pay for it.
9.4.1
Euthanasia may be considered a legitimate emergency treatment of an animal (under the definition of an "appropriate treatment" in subsection 9(1)(i) of the PCA) in those circumstances where it is impossible or impractical to provide for satisfactory alternative treatment, and where indicated by the registered veterinary practitioner's clinical examination.
An owner and vet can come to an arrangement in regard to costs involved in treatment versus euthanasia, but a vet cannot choose to euthanase on the basis of payment for services. Payment is a civil matter and nothing to with the Act especially if the owner authorises treatment and commenses a contract to treat the animal appropriately. The same applies if midway through treatment the owner runs out of money, the vet cannot euthanase the animal as an alternative to providing a treatment regime on the inability to pay basis, or return a partially treated animal to the owner knowingly that suspending the treatment will cause the animal to suffer. Although vets from a business perspective try to avoid these situations, money is secondary to the appropriate treatment of an animal and is one of the reasons so many vets get caught up in non payment situations.