There are a few different "types" of pheasant hunting that get lumped together under the umbrella of "South Dakota Pheasant Hunting".
Type 1 - Public Land, One Dog, One Man - A lot of guys here on the forum, such as myself, find the most satisfaction hunting alone with the dog on public land. For me, it is the most challenging/rewarding type of hunt. I would include guys who come in groups and exclusively hunt public ground in this type. As A5 mentioned, the likelihood of encountering pen raised pheasants is small.
Type 2 - Private Land, Non-commercial - This is what used to be the standard for many years. While not as common, there are lots of landowners who have the group of hunters/descendants of those hunters come out each fall for a pheasant hunt. Additionally, this would include locals and non-residents who access private ground through personal connections and while there is gifting that occurs, it typically is not transactional and is done with true generosity. It is possible to knock on doors and get permission to these places. Again, it isn't as common as years prior, but it isn't a unicorn either. These landowners are rarely going to be releasing pheasants as there isn't a need or reward for doing so.
Type 3 - Commercial Preserves - Quasi-commercial/Transactional hunt. You pay money and they make sure you get to pull the trigger. Personally, I feel this violates the foundation of hunting as there is never a guarantee in hunting. But, that's me and as a guy with some strong libertarian tendencies, what people do on their own land that doesn't encroach on my freedoms is something I just have to deal with. These are the places where nearly all pen raised/released pheasants are going to be found. And with the exceptional habitat these locations provide, there are likely plenty of wild pheasants around, at least in the early part of the season. Basic math would indicate that after 30 days of 10-20 hunters shooting piles of pheasants, the repopulation with pen reared birds is going to drop the likelihood of a wild pheasant being harvested. And as I alluded before, a pen raised pheasant can end up on public land, but any business minded individual is going to do their darnedest to keep their $20 investment (more like $25 for this coming season from what I've heard) in front of their clients, whether they are a preserve or a landowner who has a couple groups of hunters come through each fall.
That's my basic view of the matter. If you come to South Dakota and hunt public land, maybe knock on a few doors and get permission on private land, you are rarely going to encounter a pen raised bird. If you go to a commercial operation, you will find wild and pen raised pheasants and the later in the season, the scales will be tipped and a person is going to find themselves shooting pen raised pheasants.
So, is South Dakota just hype? That all depends on the type of hunting you'll be doing. Showing up to South Dakota to do a public land hunt and being unfamiliar with the properties you encounter might not be that great of a time if a person is expecting to see pheasants explode from the cattails like locusts. But if a person comes in with the mindset that they will hunt hard and hunt smart, tempering those expectations, there is no doubt that South Dakota offers one heckuva good opportunity.