I believe that airlines have been allowing what are termed "emotional support" animals to fly with their humans. There is a definite distinction between the emotional support designation and "service animals". Service animals have been trained to to do work or perform tasks for people with disabilities. The work or task a dog has been trained to provide must be directly related to the person's disability.
DW & I know several acquaintances and even a family member that have been able to get their M.D.'s to declare their dogs as "emotional support" animals for the sole purpose of taking their dogs with them on trips. I take it then that Delta will no longer permit "emotional support" animals on their aircrafts.
Last May, when flying home from Paris - we had a lengthy conversation with a flight attendant. She inferred that animals had greater rights than paying customers. Further, she explained to us that if no additional seats were available on the flight and an animal was the nuisance (neighboring passenger was allergic) - the animal gets to stay and the passenger would need to be rebooked on the next flight.
We did not like the policy, BUT it gives us an understanding to Delta Airlines corporate mindset.
I'm glad that they now have retracted that condition and are formalizing a process to handle the transportation of pets.
I