Therapy dogs, Emotional Support Animals, and Service Dogs are all very different.
Therapy dogs visit people in nursing homes, hospitals, schools, etc. and provide comfort to those other than their handler. They must be invited to these places and have no public access rights.
Emotional support animals, what I'm assuming this woman is asking about, are allowed to live in places that may not otherwise allow pets. They are also allowed to fly on airplanes. They are not allowed in stores or any other public places that don't allow normal pets. They don't have to have any formal training, just a doctor's note saying it's necessary for the person to have the animal.
Service animals are task-trained dogs that mitigate a handler's disability. These are the only ones that are allowed in public places. They must undergo intense training.
Now as far as if it is ethical for a doctor to write a letter saying her dog is needed for emotional support just for her to get around the size restriction, I guess that's up to the ethics of the individual doctor...
So many people fake all of the above types of dogs and cause so many problems for people who really benefit from them.
(I'm a puppy raiser for a service dog foundation so I have strong feelings about this topic.