You also cannot use private property rights to destroy the right to keep and bear arms. Both of these are fundamental rights and must both be recognized.
There has to be a balancing of rights, and it seems to me that a private property owner has the right to determine who or what comes on to his property. Forget that it's a company. It's still private property. Think of it as your own home and tell me what say you have in determining what goes on there. You can invite people in to your home but you can dictate on what terms they can come in. You can say they must remove their muddy shoes, or they have to leave their dog outside, or they can't come in armed if you don't want them to. You have the say. It's your castle. How can I be wrong in this?