The government isn't stifling Fox's speech here. It is merely saying, "you can't film here for commercial purposes right now."
I didn't say anything about “unfettered” access. It is my understanding that governments may impose reasonable time, place, and manner restrictions on access of the press to public property, but these restrictions must be content-neutral. So, Cornell can't allow, for example, HuffPo or the NYT to conduct on-campus interviews and then deny the same access to Fox. And, with a few specific exceptions (jails, grand jury proceedings, closed-door government personnel or land-acquisition sessions, active roped-off crime scenes, etc.) “reasonable” restrictions can't be 24/7 and applied to all of the public property.