I'm sure they will have some kind of claim check system now, and if they actually enforce it, I am sure people will get angry when they lose the claim check. You ever been questioned or carded when picking up your animal from the vet? or a groomer? No one expects someone to lie about whether it's really their dog, especially when they have to pay the bill to pick her up.
How many times have you been given a claim check and returned to pick up film, your laundry or whatever where they actually require the ticket? You give them your name, they go look for your stuff. This is no different. People don't expect theft like this till it happens. Once, and the rules then change for everyone, for awhile.
I dunno, all my experiences have been with vets or shops small enough where we knew the personnel and so this couldn't happen. That's not to blame the owner for leaving her pet with a large shop, but after this story I would certainly be leery of such without a claim check system. You do raise valid points.
It seems to me this isn't the first time I've read about a Petco giving a dog away to the wrong people.