All research the university does is different than all research the professor does.

As long as they are at a university being funded by the public, the public has a claim to the research. If they want to do private research, they can switch to the private.

If a person is being paid by the public, why should they be able to spend their time and resources working in private? Think of it like a general IP ownership agreement at work. Anything you create at work, using the tools your work provides, belongs to the one paying you. Now claims like any similar work you do even after you leave, or work you do on your own equipment on your own time are unreasonable, but I see nothing wrong with that requirement while being paid by the public and using equipment paid for by the public.