One of the shelters in our area worked out a deal with our Vet. The shelter provides a voucher for spay/neuter at the low shelter price with the surgery performed at out Vet's office. We took advantage of this for one of our girls when it was obvious she was not a good enough working sheepdog worthy of being bred. The shelter provided the voucher when we were at a rabies clinic provided by the shelter.
I would not be surprised if our Vet provides his services at cost (or only the costs of the supplies) and the shelter pays these costs through their funding sources with the pet owner paying a nominal fee.