I do not believe the G&F releasing birds is true, but this is:
It is well known and even documented on the SD G&F site that licensed preserves release around 500K birds per year. Private land outfitters (not preserve) can and do release many also. When some high end hunts can run $500/day or more, the owners want these guys to shoot limits. Many use acreage and habitat, others rely on supplementing the roosters as the season progresses.
If you are on a paid hunt and see roosters out number hens by a large ratio, notice flared nostrils or damaged tail feathers on the deadbird, suspect release.
Many hunters visiting SD simply do not care if the bird is wild or pen reared, others do ... simply buyer beware when you visit these places. Ask.