There is nothing prohibiting private businesses from banning open carry either. Again you have no right to carry a firearm into a place that you don't own if the owner prohibits such carrying, regardless of the way you choose to carry it. Government entities are prohibited from making such laws and regulations, but not private entities. I don't think you have a firm grasp on how constitutional rights, property rights, statute construction, and so on work. There doesn't have to be a law endowing a property owner with the ability to prohibit open carry, the lack of a law prohibiting such gives him that right. As said before there are laws prohibiting a public accommodation from refusing admittance or serving a protected class, but there is not law requiring someone to allow admittance or being required to serve someone carrying a gun.