The U.S. Department of Justice defines disability in the Codes of Federal Regulations:
"Disability means, with respect to an individual, a physical or mental impairment that substantially limits one or more of the major life activities of such individual; a record of such an impairment; or being regarded as having such an impairment."
The "third prong" is "being regarded as having such an impairment."
The premise is that even if a person isn't disabled, if they can convince others to think they are, perhaps by telling them so and using a service dog, then that makes the disabled under the ADA and they actually do qualify for a service dog. Yes, it's circular logic and not actually true.
Several courts have ruled that a service dog must be individually trained to perform tasks that mitigate the disability of their handler. Without an actual disability, there is no disability to mitigate, and no tasks that can be trained that mitigate the non-existing disability. Without trained tasks that mitigate the disability, the dog is not a service dog.
The ADA wasn't meant to create a privileged class that has rights over and above those of other citizens. On the contrary: it was created in an attempt to give those with fewer rights than other citizens a leg up to a more equitable existence. A blind person who uses a guide dog is using that dog to compensate for his lack of sight. A guide dog is a poor substitute for actually being able to see, but it is one of the better compensations available. Legitimately disabled people would gladly retire their service dogs to pet status in exchange for being able to do for themselves the simple things in life that everyone else takes for granted.
People mean-spirited enough to dig for a ridiculous loop hole like this one deserve every legal consequence of impersonating a person with a disability in order to gain rights or benefits not due them. Fortunately, there are laws in place to punish such people with fines, prison terms, and/or loss of future benefits (such as Medicare, Social Security Benefits, Food Stamps, etc.).