Most likely you have never heard the phrase "computer says no".
Here, the Hammerbarn are trying to identify people who have been banned from their shops. Even if it's not an issue now, there will absolutely come a time when the security are confident enough in it that they'll assume it correct by default.
Now, note that I said "Even if it's not an issue now", because... well why did the authorities start investigating? There is nothing in the story to tell us why, but presumably someone complained, but simply hadn't tweeted about it or spoken to local papers.
We can only speculate about what happened, but I personally think it's a reasonable assumption that a customer was stopped by a security guard and would have been expected to provide proof that he wasn't the person the computer thought he was. i.e. he would have had to provide sensitive personal information to even just go in and buy a roll of masking tape, which doesn't really seem particularly fair, because no-one else does. If I have to prove I'm not someone who bears a passing resemblance to me, that's basically presumed guilty until proven innocent.
People may talk harsh about public bodies sticking their noses in where it's not necessary, but public bodies generally don't do anything until and unless asked to. We don't know what the complaint was, and I think my speculation probably describes a likely scenario that is definitely far from the worst case scenario. The fact that the authorities didn't give out details shows that they consider the complainant's data protection rights to be important -- more so than the retailer does!
But on a tangent... we are, as a culture, too quick to judge people who make decisions we do not immediately agree with. As a result, we're developing a situation where people are more and more having to justify their stance, and while that sounds good in theory, when we start having to publish the public complaints that started it off, we're only going to start discouraging the complaints in the first place.