You miss the point (which is actually the focus of the headline).
The violation of rights is demonstrated in the criteria used to exclude people.
Selecting against pyromaniacs when granting access to the gasoline is a false analogy.
A better analogy would be an employer (government or private) preventing anybody from distributing any sort of non-work-related literature while at work. That's permitted.
But the emloyer could NOT specifically prevent people from distributing political literature that was pro-union.
Note again that the violation is not in the prohibition, but in the criteria for selecting what's prohibited.
By selecting against malcontents, you are specifically excluding those who would seek to exercise the right to petition for redress.
The right to petition does not stop at "If the carefully selected lies we choose to present to you piss you off, you can say something. Because we have already prepared glib answers to shut you down, and, really--if we cared what you say about those issues, we wouldn't have let you know in the first place."
The right to petition also includes "You get to see what we're doing and judge for yourself whether you have a grievance."
A completely separate argument "it's an issue of national security" is code for "we've told a different lie to everyone involved. We would be quite embarrassed if you people got together to compare notes." God help us if you actually found out what we do here--you'd be pretty angry about it.