It's okay, even doctors get sick.

However I tell them I want a letter from their  doctor with his letterhead stating that this specific dog is a service animal.

Or maybe he meant $100,000 in gross assets notwithstanding the amount of debt you have (which might be relevant for doctors, dentists, lawyers, and other professionals that have larger student loan debts). 

My doctor told me that 99% blockage due mostly to stress almost killed me without warning.

@Caroline Hedin  think also about your doctor or dentist calling you the day before your appointment... reconfirming is their lifeblood.

Unfortunately you can get a doctor anywhere that will sign off on the need for a "Companion Pet" and a lot of tenants know this.  

Doctors are literally seeing people via phones and tablets nowadays, even prescribing medicine.

Doctors tend to want latest and greatest for build outs to commit to a space.Are you paying all cash?

When I heard that and only after they gave me a verbal commitment did I ask if she had another doctor friend that might have an interest.  

My understanding is there is no pet deposit, no additional pet rent, you have a right to ask for proof as in a doctor's note or something, but  you can not decline the tenant because of the dog and you better have a good documented reason if you do decline them for that really good reason (that has nothing to do with the dog) .