Well, it obviously doesn't mean jack if you have a HCP, as far as a loaded handgun is concerned.
Certainly you can have an unloaded long gun, with ammo well separated, in your vehicle, just as you can anywhere else in TN, including a National Park, where permitted hand gun carry is not quite yet legal.
I lean toward the notion that if you have a HCP, you could also legally have a loaded long gun in the vehicle in state park also, but I'm not the TN Attorney General (I have much more common sense than he).
Remember, that whatever "no guns" signs that are on the side of the road in state parks were not mandated to be removed or modified with the passage of the state park carry statute. And I'd reason that their website is the same old wording also.
- OS