We agree.
Second, their property rights are being respected because this is not a law that allows them to carry into the building at work only the parking lot. If there is a private property rights issue it would arise from someone telling you what you can and can't keep in your own car. Many States have laws that treat parking lots that are private property but open to the public as public property in certain respects-- police ticketing handicapped parking violations for example.
This is an interesting perspective, but I remain unconvinced that parking lots are not private property. The fact that the government does not respect private property (by regulating parking lots in other ways) does not mean that parking lots are public property, any more than private wetlands are public property because the government unjustly tells the owners how that property can be used.
Without this law, people are required to travel to and from work unarmed. Just think about your own daughter leaving a remote workplace at midnight and the issue takes on a whole new light.
I would simply tell my daughter not to work for that dangerous employer, just as I would tell her to not work at a steel mill with a history of avoidable accidents. If she chose to ignore me, I'd have to respect her decision (assuming she is an adult).