Becuase the university signs my paycheck, not the state. Some of the money to fund me comes from Federal grants, some from federal contracts, some from private contracts, some from private donations and some from state funds. (I work on several projects). So while the institution is subject to state regulation, and can be claimed by the state it is a separate entity. Thats why claiming government is wierd, it is not the only source of my income. Most people in academia have a similar mashup of funding.
If your paycheck comes from a government organization, then you work for the government.
If you were a software engineer for the government would you complain that you can't state that you work for a business?