Back to the original OP subject: So it does seem to be left to the propetry owner for the decision.
1.) I worked with an avid firearms guy who walked into a popular restaurant in a popular forest destination town here in AZ. He had a small firearm holstered on his side. He and his wife sat down ordered and just as his food arrived at the table a police officer came up and asked him to please step outside. The officer said that he was called because my friend ignored the request of the restaurant not to bring weapons inside. My friend asked the officer how he was supposed to know this as no one mention this nor were there any signs.
So the officer brought the manager out who could not find the sign. After some searching by other employees they found that the tape had come loose and the sign fell down behind one of the booths. The manager apologized and offered a comped meal. My friend asked why he didn't come by the table to ask him to remove his weapon. The manager said it was their policy not to approach gun wearing customers. They were instructed to act like business as usual and call the police. My friend left his meal on the table and left for another eatery.
Next has to do with carrying a weapon in your car while in you work parking lot. I worked at a very large manufacturing firm that had a policy against weapons on the property. The entire facility and parking lot was fenced & gated with signage prohibiting weapons. When I started there the security personnel were armed, until that department was outsourced. There where a few times where ex girl friends would tell HR or some one in the security office that there ex had guns in their car. Security would then call the police and that car would be torn apart looking for said weapon. This happened twice while I worked there.
Employer #2 had the same policy but no fence, gates or signs. Folk who would usually carry did complain that this meant they would have to ravel thru a bad part of town without protection. Management simply said that there would be no car searches but they would nut change the handbooks. So we were to take our chances either way.
My next employer had a no weapons policy when I started but that changed soon after due to the HR manager being an avid shooter. The new rule moved all signage to the building doors. Folks were allowed to have one weapon of their choice in their vehicle. However they were no allowed to enter their vehicle for any reason while on the clock. As for me, I worked nights and had to deliver parts to the paint shop across town in time for the morning shift to paint. This facility happened to be in the absolute worse part of town. I had even had the police show up to tell me that it was not safe for me to be there...on several occasions. After telling my boss this he agreed to allow me to carry as long as I didn't advertise it.