Carrying not allowed within state parks of which their land is leased from US Army Corps of Engineers?

Just found out a state park I may travel to in Texas has their land leased from the federal government, and the state park office employee said concealed carry isn’t allowed, along with even having a gun in your car. Is that information correct? I guess if the land is owned by the fed government it trumps my TX LTC? Anyone know the penalties of carrying within a state park but technically on federal land? Kind of confused on what laws apply here.Thanks. via /r/CCW https://ift.tt/2uVTYJN