They can save face that way, but you still get what you want, and the relationship isn't destroyed. 

Threatened with eviction they fled (with their hardware) and we had to put hvac back together. had a client whose house was basically destroyed by an indoor grow..  

Let them move out and be happy you don't have to go through an eviction or give them cash for keys after their dogs destroyed the house.

We only deal with termites or other wood destroying insects.

Deny the animal and a judge will rule against you and destroy your business. 

And being able to be more choosy will let you get tenants less likely to destroy the place.

I had a tenant in a year destroy a new carpet.  

If you are getting rent and she is not destroying the property that would be considered a plus.  

They will usually verify dates of tenancy, but not that they were asked to leave or had raging parties or destroyed the place.So, you have to really gather as much data about them as possible and get your info in other ways.Check their social media accounts, too, if possible. 

Just like all squares are rectangles, but not all rectangles are squares.If it looks like a duck, and it walks like a duck, and it quacks like a duck, it's a duck.If by some miracle I were to make a get-rich-quick scheme like that succeed, that's the kind of unearned luck that can turn around and destroy lives.