"A public place is generally an indoor or outdoor area, whether privately or publicly owned, to which the public have access by right or by invitation, expressed or implied, whether by payment of money or not, but not a place when used exclusively by one or more individuals for a private gathering or other personal purpose."
US airports are public places. Just because it is private property doesn't automatically mean it's not a public space. If you turn your home into a B&B, it becomes a public space, even though it is your private property. You can have private clubhouses and private airports but the moment you leave the door unlocked and put up a sign that you're open to the public, the presumption of privacy is gone.