While the basics of the story have been verified by the police and Braehead, I wonder on the specific details by the father.
Going solely by his account, the security guard and police officer were out of line - but neither of their actions is new or unexpected to many photographers. Assumptions have incorrectly been made on the law, and because these people are in a position of power, they look to enforce it.
The father, I believe, would have been within his rights to ask why he was suspected of falling under the act and the officer would have been obliged to say.
Neither officer nor guard had any powers to demand pictures being deleted [although, only the guard did that]
Having shopped at Braehead many times, I have never noticed any "no photography" signs - although I will be on the look out for them now, and checking how new they look - but their website does mention this rule. Visitors cannot be expected to have checked this, however.
The big 'but' here comes with what really happened? How much was embellished or omitted from the story? We don't know this guy, so he could have flipped a little and thought nothing of it, believing he was being reasonable. Was the security guard initially polite, or was he obnoxious from the get go?
