Probably a doctor and not an airline should make the call? It seems like a useful principle that airlines should not be in charge of medical decisions, which would imply that airlines should never question traveling with a horse (besides checking the doctor's authorization) - if we think that someone is being overprescribed a horse, we-as-society should follow up with the prescribing doctor and perhaps medical licensing boards, but we-as-society shouldn't put indirect pressure on the doctor via the patient themselves via a flight attendant.