I find this story appalling. It is beyond insulting to people who really need and use a service dog and puts everyone at risk if this dog is as untrained as you say. I was under the impression people with the need for these dogs had to make application for one through a small group of organizations that train and match up dogs to people who need them. If that is indeed the case they must be furious with these phony online deals.
No, you don't have to get service dog from any particular source. In fact, many service dogs are bought by a person who needs one, and trained specifically to work with that person. I was just alking the other night to a woman who has a Basenji who is her diabetes service dog. The dog has saved her life on a number of occasions by alerting her to changes in her blood sugar before it became dangerous. That dog is now 10 years old, and she is also working with a younger one who will eventually take the older girl's place. I know a number of service dogs who have been privately trained.
This subject comes up on a regular basis in training circles, because it drives ethical trainers crazy that unethical people pretend their dog is a service dog, just to get them in places that pet dogs are not allowed. But there are no laws governing how service dogs are trained for good reason. There are many, many disabilities, and even among people with the SAME disability, their needs in a service animal can be quite different. So the training is quite specific.
Store, restaurants, etc. cannot ask what a person's disability is, nor can they ask for any "proof" (since there is none... An almost certain sign that a "service animal" is NOT legit is if the owner has some "card" saying they're a service animal!) they CAN, however ask what specific tasks the dog does for the owner. (Such as detecting changes in blood sugar in the woman with diabetes, picking up items dropped on the floor for someone in a wheel chair or guiding a blind person)
I am priviledged to have seen a number of these dogs in training, because my training center provides specialized training for service dogs, specifically for people with MS.
Oh, forgot to add that no business has to put up with a "service dog" (real or fake!) that is disruptive or causing problems for others. They are within their rights to ask the person to leave with their dog if the dog is not behaving properly for the setting. (Which generally means lying quietly by the owner's feet unless they are actively working)