It is really a state by state law concerning comfort animals and housing. If the landlord has it in the lease, they usually are covered as long as it is not a service animal.
A lot of landlords will not want to put up with the legal fight, so they stay quiet as long as the animal is well behaved and housebroken. It truly depends upon the state laws. As a disabled individual, I really wish that there were federally uniform laws concerning service and comfort therapy animals. Comfort animals should undergo certification, just as service animals do, to prove that they are well-behaved, housebroken, and not going to impact anyone else. There are many therapeutic benefits that both provide but the reason that service animals are afforded the rights they have, is because they do undo such strict standards and certification.