From the few facts presented, Southwest made a reasonable decision.
While led many support animals are phony, many more provide a real service. The ADA laws on this are outside Southwest’s control, right or wrong. On the other side is a passenger stating an allergy without any medical documentation.
Given these facts, Southwest made the best decision possible under the circumstances.
While note really relevant, if I had a life threatening allergy, I’d be sure to discuss it with the airline when making the reservation. That would have avoided the problem since documentation could be brought and Southwest could have known not to book the pets.