Hey LM, thanx for the great introduction. I'm flattered

Do you know what I do for a living? I own a street sweeper company. And while we only do large scale construction and municipal size work now, yet in the past did a LOT of shopping centers. You know, the night-time little vacuum trucks that run around all the shopping centers, strip malls, etc.... And because of that (having also to clean the alleys, truck ramps, etc... ) we had "carte blanche" to all the dumpsters in town. They were where we had to dump the contents of our sweepers afterall. And where we put the garbage bags from the sidewalk trash cans, etc... So I became an expert in dumpster diving. And dealing with paper work issues, became versed in shopping centers, management co's, tennants, etc.... So I am NOT un-versed in commenting on this question
Now of course, our access (legitimacy in being around dumpsters) is not the same as "Joe Blow" snooping around. But ....none-the-less, the background affords me a good look at the issue.
Yes shopping centers are "private property". And as such, they even have little signs at the entrances (which no one ever reads) saying something to the effect of "private property. Permission to pass revokable by owner" , etc.. Yet despite being "private property", ....... last I looked ....... there was no shortage of people simply helping themselves. In fact, I bet even LM has gone on to a shopping center in the past week, without having "asked" (gasp). Not sure who posted his bond, or paid for his lawyer.
So here's the deal: if someone came out of the back door of the Radio shack and said "scram", then yes: that becomes an issue of "revoked by owner". Then yes, if you persisted, they could call the cops, and then yes, you'd be in legal trouble. But so long as you obliged and left, well then .... ok.
Not sure about other places in the USA, but where I'm at, people looking for moving boxes will ROUTINELY go to store dumpsters. And the stores actually welcome that (and will, in fact, set them out their back doors un-crushed HOPING that people come take them), because it decreases their amount of trash/space in their dumpsters. I'm not trying to say that stores welcome dumpster divers who take an hour to snoop through all the entire dumpster, because of course that a) merely conjures up images of debri left all around the sides of the dumpster, and b ) conjurs up images of someone getting hurt.
The stores actually throw a lot of darned good stuff out! I used to make a substantial side income dumpster diving, by collecting all sorts of cast-offs, and .... 1x p/month going to the flea market

You know, crazy things like the drug store chain would have a big dollar day sale, and .... at the end of the day, pitch all the cosmetics and stuff that didn't get sold. Or the samplers that didn't get passed out, and so forth. Or cases and cases of cigarrettes that passed their expiration, yet are still perfectly good. Or product packaging that got damaged, yet the product inside is still good, etc....