Yes. Some hotels offer government rates to federal and state government employees while others offer these reduced rates only to federal employees. Before reserving a room at a government rate, check the terms on the hotel's site. If the traveler does not qualify, the reduced government rate may not be honored at check-in.
UVA employees may book a state government rate if booking a hotel within Virginia. For hotels outside of Virginia, UVA employees will not qualify for the state government rates.