Yes, this scam was very popular for a while in the USA. People would go online and buy a certificate, sometimes even from an "MD", that their beloved pet was a service animal, and therefore had to be allowed on airplanes, in restaurants or shops, etc. You could buy little "service animal" vests for the pet.
For airplane travel, it would allow the person to bring their pet into the main cabin for free, to be with them, rather than in the cargo hold below. Of course, many times these so-called service animals were unruly or ill-trained. People became resentful over what was clearly an abuse of a good concept (same thing with people using wheelchairs to get onto planes early to snag the prime seats, but that's a story for another day).
Because of certain US laws on discrimination, the airlines couldn't challenge the person by asking what medical condition they had that required them to have their pet designated as a "service animal".
But I think the airlines have started to clue in, and are taking measure to ensure people don't abuse the system anymore.