A pet policy does not apply to an assistance animal
Federal fair housing rules generally require reasonable accommodation for assistance animals, which means a no-pets clause and pet rent do not operate in the usual way. Owners who treat the two the same create a fair housing problem for themselves, and that is a far larger exposure than the animal.
Your carrier may restrict breeds anyway
Where an insurer excludes certain breeds and a tenant has a qualifying assistance animal of that breed, the owner is caught between two requirements. It is solvable by choosing a carrier without breed restrictions, and it has to be solved before the situation arises.
Liability for a tenant’s animal can reach the owner
Arizona imposes strict liability on dog owners, and a landlord who knew of a dangerous animal can be drawn into a claim as well. Knowing what is on the property, and carrying real liability limits, is the practical protection.