Are commercial stores private property, though? In several instances they are treated as being public property--ADA enforcement comes to mind. Right of entrance comes to mind (With certain specific exemptions). Discrimination laws also apply.
However, they are owned by private individuals or companies. I'm not sure what their status legally is--does it change from instance to instance?
They have positioned themselves as essentially a public place by allowing the public in without membership. I do know this brings in various aspects of the law. For example, go out on your private farm and flip your car, getting hurt. I don't believe you have to call the police for that. But you do in a public access parking lot even though it is private property. This issue has come up in malls quite often, with the right to free speech butting up against the rights of the property owner, with free speech generally winning (varies by state though).