Technically, the only permit you need to build a golf course is a grading permit, usually obtained at the county level. I suspect that some rural counties don't have such a procedure, although it is fewer and fewer of them today.
The county is the body that then decides if there are aspects of the project that require approvals from the Corps of Engineers, U.S. Fish & Wildlife, or other governmental agencies, before they grant you the grading permit.
Usually, if there are wetlands in the area at all, they will require you to hire a local engineer to delineate the wetlands, and if you want to make any changes to [or close to] the wetlands -- or build any bridges across them -- then you have to deal with the Corps. But, I've built many courses where we did not need a permit from them.
Pikewood National does have a couple of water features, so it's possible they skated by a rule, but it's also possible the county approved it.