What are you talking about?
The government can absolutely pass laws prohibiting you from entering a privately owned location. There is no constitutional right of access to private property.
And more specifically, the commerce clause of the constitution allows the government to regulate air travel, which means regulating airports. The fact that they're privately owned doesn't change anything. If a private airport owner allowed you to proceed through security, they'd be breaking the law.
There's no public access doctrine for airports the way there is for streets or parks.
You clear seem to wish it was otherwise. But it's easy to do the research to understand where the authority comes from and why it's entirely constitutional.
Constitutional right of access, which as you say doesn't exist, isn't the same as allowing access but conditioning it upon you relinquishing your bill of rights.
If the difference between access and not having access is relinquishing your civil rights, then the reason for denial is exercising your civil rights. Those are explicitly protected. So while you're right they could make a law that says 'no one on the plane' they cannot make a law that says "everyone on the plane except those who won't give up their 4th or 5th amendment rights not to answer additional questions."
There have been prior SCOTUS cases narrowly allowing asking name, DOB, addresses, as well as inspection of your items during certain inspections, but this is something entirely different beyond that asking further probing questions about your identity.
And that brings us back to the tagline of the article:
The TSA is violating the law, and the constitution, and making it up as they go.