I guess it would depend on if you could prove the therapy animal provides a 'service' for your 'disability'. Example=Someone with Agoraphobia (fear of open spaces) using an animal to help keep them calm on the train.
From what I understand, one of the requirements is that the service animal must provide a constant service, and not an occasional service. So, an animal that only provides a service in very specific circumstances such as giving comfort only when in an open space or only when in a closed space, would be only providing an occasional service and not covered by ADA.
That is exactly why I used that example. I think using an animal for comfort, would not be a service animal, but Amtrak gets to make the decision. Since Agoraphobia is a medical diagnosis, they may allow it, but only Amtrak could answer that question. I think that would be a stretch of the rules.
Service animals are totally different than a Therapy animal. My daughter used to bring her dog to her job at a Nursing Home
for therapy for the residents. The dog was always welcomed by the residents, & missed when she had to go home.