US Department of Transport legislation regarding "non-discrimination on the basis of disability'' required all airlines operating to, from and within the US, must carry service dogs.
Service dogs included guide dogs, hearing dogs and psychiatric service dogs.
"Where a passenger seeks to be accompanied by a psychiatric service dog...they must provide documentation from a licensed mental health professional treating the passenger,'' an airline spokeswoman said.
The service dog policy applied only on flights to and from the US and not to flights to or from any other jurisdictions or domestically, the spokeswoman said.
Ms Southan said she had never seen uncaged dogs in a plane cabin before.
"It was quite unusual to see. I don't know where they went to the loo because it's a long flight.
"They weren't running around or anything or even barking, they seemed quite content.''
Jones has been seen on New Zealand screens hosting US X Factor. He was axed after two seasons.
Jackson, a model, posted photos and videos of the dogs - and their premium travel arrangements - on social media websites with captions including "first class Franny'' and "pooches on board''.
See Ms Southan's review here