The situation in Texas is unclear.
It is worth mentioning Texas as a state where the law may require statutory authorization in order to copyright state documents. Although the statute does not explicitly state such as a requirement, it can be inferred from an attorney general opinion.
At a bare minimum, the Department of Health, the State Preservation Board, the Water Development Board, the Department of Motor Vehicles, and county governments all have statutory authority to hold copyrights.
In your specific case, there's an additional complication. Something is only a work of the State of Texas if one of the following is true: 1) it was created by a government employee as part of their job duties, or 2) it was a work for hire. It's quite likely that neither of the above is true for a student newspaper, rendering the question of Texas-owned copyrights irrelevant.