Strictly speaking, the state of Texas doesn't own the gold. The gold forms some of the endowment of the University of Texas system and actually belongs to the corporation that the university set up to manage the endowment. So the gold really belongs to the University of Texas Investment Management Corporation as manager of the endowment fund.
...and I would think they’d have NONE at the Federal Reserve!
They don't. The New York Fed stores bullion for foreign governments, central banks, and some international agencies. They don't store bullion for private corporations or individuals.
The persistence of what is apparently an erroneous explanation of the gold storage can be blamed on Gov. Abbott’s office:
http://gov.texas.gov/news/signature/21038
...The law will repatriate $1 billion of gold bullion from the Federal Reserve in New York to Texas...
Thank you for that important information!