Yes. University Drive is also known as U.S. Highway 380 and part of the state highway system.
To explain more, here's a rerun of Insight Denton from June 2017, when a reader asked a similar question about trucks traveling city streets:
In addition to the state highway system, dozens of city streets also are designated as truck routes by the city engineer. You might find some of them surprising: Bell Avenue, Eagle and Mesa drives, Bradshaw and Prairie streets, and Colorado and San Jacinto boulevards. Police officers have the authority to pull over a truck driver and determine whether he or she is following an acceptable route (including for deliveries). The penalty for violating the provision is a misdemeanor, with a maximum $200 fine.
Find the full list of truck routes online at bit.ly/2zkeu5S: City of Denton Code of Ordinances, Operation of Vehicles, Division II. Trucks and Truck Routes.