Those of us in the "fancy" as it's called, are aware of these rings. Due to very strict, and actually pretty well enforced, animal importation laws, there is a large market for smuggled or stolen exotic pets. Like drugs, the laws seem to drive up market prices while not actually accomplishing much in terms of possession and "use" of the same. A lot of store that have parrots display them on stands in the store, and people can walk up and handle them, which is how I became interested 25 years ago, and the endearing quality of being able to be handled also means it's easy to walk away with one. They are kind of tough to put security tags on, they have a tendency to chew them up.
I am actually more open with total strangers about owning guns and having a CHL than the exotic pets in my home.
I used to shop in the Petland in Naperville quite often. Had a customer in the store panic when a lizard she was holding, about $2000 retail, opened its mouth toward her, and she dropped it. It scooted out the door (those things can book when motivated) and crawled up into the engine compartment of a car in the parking lot. When the owner of the car showed up to find her car surrounded by folks trying to retrieve said lizard, about 3 feet long, she wouldn't believe it was in there and was going to drive away. We finally got her to pop the hood and look, and there he was in all his glory.
I can't imagine stealing a Quaker, though, there is a wild colony of feral ones up in that area and they are considered the flying equivalent of rats.
I had a friend who owned a shop in Schenectady NY who had ALL of her birds except nestlings loose in the store, and she had airlock doors to prevent the birds from flying out. People, like me, would go in just to browse and play, so it wasn't unusual for there to be 4 or 5 people there at any time, whi were just wandering around looking, and this wasn't in a mall. One day Terri, her daughter, was minding the store and this guy came in wearing suitable business attire, up to a London Fog raincoat. Terri was "helping" a young lady clad in jeans and a t-shirt with several items and was distracted, when all of a sudden she heard one of the store pets (not for sale) yelling "Help! Murder!" over and over and she realized that another of the store pets "Rory" was not in evidence. The guy in the trench coat was exiting the store just then.
Terri followed him out in the parking lot, while calling 911, and confronted him, and when he ducked around her and got into his car she and another customer blocked his exit until police arrived. The cop asked the "gentleman" to exit the car, and when he did, the inside pocket of the London Fog was heard to be exclaiming "That's nice, Rory, go to sleep good baby."
He was arrested, but his accomplice, the t-shirt girl, took off with the items she had been shopping for and not paid for, no pets though, during all of the fuss, but was seen. It turned out that she was the girlfriend of the guy and she wound up under arrest too. Connections were made to a bird theft ring, Rory was due to be sold elsewhere for about $10,000.
Rory is a Hyacinth Macaw, 40 inches full grown, and just a fledgling when this happened. Joan, his owner, would snuggle him up each night at home, and rock him to sleep in a little hammock thing she made, saying "Nighty night, Rory, that's nice, go to sleep." So Rory was perfect comfortable in the modified pocket of the London Fog.