But they should make it very clear, and even then they can simply ask the person to leave and ban them if they so wish.
They also have to consider WHY they would want to implement such a ban, given everyone takes photos these days. Your mates on a day out (whether that's on the street, a bus or in a shop), taking a photo of a product to show someone later on (is this the one you wanted?', 'what do you think of this?') or something funny.. Goodness, there are a million reasons that aren't for any commercial gain.
They can't call the police or ask to see/delete the photos. If they wanted to do that, they could take a civil action against the 'offender'.
Whatever the man was trying to take a photo of, it doesn't change that fact. No shopping centre is going to be able to get someone arrested for breaching a rule they've set up that isn't law.
The next time security pick on a teenager taking a picture of their mate with their BlackBerry, I wonder how the media would react then a security guard started getting all heavy, and no doubt succeeding in getting the person to delete the photos or hand over the phone.
Like with Dale Farm, you make the rules and you must enforce them for everyone or nobody.