He has since added doctors / attorneys / etc as clients to manage their properties.

Greg S. has a good point about requiring the animal be certified and that you receive written proof from a third party professional (medical doctor, psychiatrist/psychologist, social worker) if the need for such an animal is not apparent and connection is not obvious to someone unfamiliar with the applicant and the animal.

His doctor prescribes John a dog to help alleviate some of his symptoms.

Only a prescription by a doctor.

Today she walks in my office, gives my assistant a note from her doctor that she needs an animal and turns away without saying anything to my assistant.I am pretty annoyed at this but it seems like my hands may be tied and I will just have to accept this animal.

I'm not sure but probably not.You can ask a tenant for written confirmation from a doctor stating they have a disability and require a service dog, but that is about it.

Would you want a doctor deciding to give you medical care this way? 

However, if you have traveling scholars/professors and or doctors, who might only be at your area for a year or two, then they might rent.  

We can't really ask for doctors' notes these days, so it's basically "stated disability" just the way things were "stated income" in 2006, but I think we both know the right thing to do is not take advantage of something intended for blind persons and people with autism, and use it for the benefit of our son who is simply lazy. 

I wouldn't want an ear nose and throat doctor operating on my heart.