Its correct.
As I understand the law open carry of firearms in government owned facilities (state and local) is allowed. They may ban concealed carry and may ban other non-firearm weapons. As I recall this also only applies inside buildings.
A crazy side effect of this law was that the Lousiville Zoo was posted but since the facility is mostly outdoors you could conceal carry anywhere outside (the main gate) but as soon as you went inside (the reptile house) you needed to be open. Since then I think they've actually removed their signs.
Part of me thinks this is a trap. If you're following the letter of the law you could carry with a jacket over your firearm in a park, but if you go into the restroom building you'd have to take your jacket off and carry openly. I'm sure someone will poop their pants over this sooner or later and claim a man flashed a gun.