Regardless of whether that would be reasonable, is it actually true? I know that the United States has specific rules for "public accommodations," which are private properties that are generally accessible to the public, like retail businesses. Property owners in this case don't have complete control over who enters their property. The obvious example is refusal of service due to membership of a protected class like race or religion.

So I'm not so sure that police will escort you out of a Walmart because they caught you taking a picture of the parking lot with your smartphone.