Even in a publicly funded property, it is still private property thanks to the incorporation of the UNITED STATES as a corporate entity. Explaining that subject area is too much for this article, but do some research on it, because that is the law of the land, in truth today.
An example though. I worked for a private company, contracted to New York State, as a security officer. We housed sensitive material on engineering of bridges, buildings, and so forth. Blueprints and stuff. We even had a geological lab in the basement. Even though it was "public" property, photos were strictly forbidden, and other restrictions applied. And with good reason I might add. (When I worked at a nuke plant, we had license to kill.)
So even though this was technically "public" property, as a guard, I had the legal right to bar you from taking pics, and to confiscate your material if you violated the rules of the property. Short of that, I also had the right to eject you from the property, and to arrest you if you refused.
This is a premise that so many people fail to understand, even at their privately owned local shopping mall, or even a publicly funded educational institution. This is also the same premise by which police claim the right to search your bags an the quasi-public subway system of NYC.
So while I whole-heartedly disagree with the intrusion of liberty here, the fact is, legally, the guard and the administrators reserved the right.
Now to put this on it's head a bit. What if that man was handing out bomb-making instructions? A lot of people would say "well, then the guard had a right to stop him."
I say bullcrap on that too tho. Free speech is free speech, after all.
The video that provoked my rant today:
Mall Cop's Fight Highlights Public Misunderstanding of Authority