The Tennessee Performing Arts Center Management Corporation is governed by a 20-member Board of Directors. Eight of these directors are appointed by the Tennessee Performing Arts Foundation (the Foundation that led the efforts for TPAC and raised an endowment to support TPAC operations). Four Directors are named by the Tennessee Arts Commission and four directors are named by the Governor of Tennessee (one of the Governor's appointees must be the Commissioner of Education of the State of Tennessee (or his/her designate).
Firearms are prohibited in all state buildings. All "prop" weapons must be approved by the TPAC Technical Director at four (4) weeks prior to load in and demonstrated to the TPAC Technical Director upon arrival at the venue. Licensee is responsible for training and safety requirements.
The statement at their website is not accurate, in my opinion. Although they do have the power to prohibit firearms on a state owned property, there is nothing in the Tennessee Code Annotated that prohibits firearms in all state buildings, across the board. Here is a relevant AG opinion:
What it is going to come down to is whether or not the building is posted in accordance with the law or not. They can't just ban because of a misleading sentence on their website.
That's my opinion and I'm not a lawyer. However, I'm not trusting the posting on their website until I see an actual citation from the TCA.
The last time I was at TPAC (back in April) they had gunbusters and signage that would have made them compliant with the previous posting law.