In theory, the company is free to ban posession of weapons in cars parked on their property.
However, without a search warrant or probable cause of criminal activity, they do not have the right to search a locked vehicle.
We have been told that we cant have guns in our cars in the UPS parking lot----but come out there on the Friday night before opening morning of hunting season and you will see dozens of trucks with campers, trailers ect. all loaded up with gear and ready to head to the hills as soon as their owners (Some of whom are management) clock off. Something tells me that there might be a deer rifle or two in those rigs.
Bottom line---its a rule, but it is not enforceable.