Webleymkv,
As a campus, I am referring to a wide area consisting of residential housing, shops, professional offices, theaters, museums, and a wide variety of actives available to the general public and open grounds available for general use by the general public, even University hospitals to serve the general public. ALL on campus. Not to mention public paved roads, water, sewer, and some provide their own electricity, phone, and INTERNET services which are accessible at any time while either on, or traveling through campus-even when no classes are being held.
These are much more then the big classroom building with a parking lot you may be envisioning. University and college campuses are much more like a town within a city then they are a typical business setting. They are public places generally used by the surrounding general public for a great number things.
Without being familiar with the area you could have gone to the bank, driven to a restraint and picked up lunch for you are a friend to meet and play football in one of the open areas, picked up a paper and met your date for a show and afterwords took a walk in the night and never known you had come onto campus. You could even get a place for the night so you can be close by for the parade and street fair the next day.
Your hospital example causes me to think your not getting the concept of general public use. Try reading the Marsh opinion if you haven't already and put in 'campus' where they talk about Chickasaw. You'll see that it fits like a glove on a hand how campuses, especially the larger ones, are run, built and arranged and what the justice state about the conpany toen in the case. Maybe the opinion itself will do a better job of illustrating the distinguishment between privately owned businesses that are open to the public and privately owned facility built and operated to benefit the public and since their operation is essentially a public function, it's owner's property rights become circumscribed by the statutory and constitutional rights of those who use it.
If a University campus were just a big building and a parking lot that's singular activity were holding class rather then of a small community within a larger municipality then the rebuttals you present might make comparing them with retail stores or a hospital might be more compelling.