Wrong. A corporation is not a "public" entity, even if shares can be bought by the public. A corporation is an entity separate from the state. A corporation's property is private property not public property.
Sometimes it is private. If it's the parking lot and there is a collision between private cars, it is quasi-public. If it is somebody on the property, restaurant or store, to buy something it is quasi-public. This is not at all clear. The corporation exists by the Constitutional authority of the FedGov, and may be owned, which is hardly the description of a private person.