In other words, they have recently admitted that 6 people are living there, but have also said that 3 out of 6 tenants are related by blood, which is legal in the county - and provided a new name and ID of a related person I am pretty sure is not actually living at the property, rather than the person whose name was on mail left easily visible on the floor when I visited - even though I'm almost certain this is false.

Which, of course, gave me a legal reason to deny them - for not completing the application or for giving me false info.So, I'd charge them something, even if it was $10.You could always say it will be refunded if they're approved.  

My bigger concern would be a tenant falsely claiming theft.

I agree below market rent doesn't do you or the tenant any  favors because it gives people a false sense of what they can afford and your business isn't optimally run. 

Know the law and don't let brokers spew false statements at you. § 42-26.

Filing a false police report is a crime.

As others pointed out, a lease can be a false sense of security because tenants will move sometimes regardless.

.- - - - - - - - - -PET AGREEMENT  (Addendum to Rental Agreement)The Month-To-Month Rental Agreement (the “Agreement”) dated_______________________ between __________________________________________________________________________, as Landlord and ________________________________________________________________________, as Tenant of real property located at _______________________________________________________, is hereby amended to include the following terms and conditions: The rental agreement specifically prohibits keeping pets and animals without Landlord permission; Tenant agrees to follow these terms and conditions in exchange for permission to keep a specific pet:Condition for keeping a pet:Tenant agrees to pay additional rent of _____________ per month for the privilege of keeping this pet.Tenant agrees to pay additional security deposit of ______________ for the privilege of keeping this pet.Name of pet: __________________________Description of pet: _______________________ (type, breed, color, age)Veterinarian: __________________________Emergency Caretaker: ____________________Tenant agrees to:1.Provide proper care for the pet in accordance with veterinary recommendations or ASPCA (American Society for the Prevention of Cruelty to Animals) guidelines.See www.aspca.org.2.Adhere to local ordinances, including leash, vaccination, and tag/licensing, requirements.3.Clean up after the pet and dispose of pet waste properly and quickly.4.Not to leave pet food or water outside the dwelling, as it could attract other animals.5.Not to leave the pet unattended for any unreasonable periods of time.6.Keep the pet from being noisy, aggressive, or from causing any annoyance or discomfort to others.7.Immediately remedy any complaints that arise from pet behavior.8.Immediately pay for any damage, loss, or expense caused to others by the pet.9.Provide pet with regular health care, to include inoculations as recommended by a veterinarian.10.Spay or neuter the pet when it becomes of age to do so.11.Arrange for an emergency caretaker for the pet.Tenant agrees to indemnify, hold harmless and defend Landlord against all liability, judgments, expenses (including attorney fees), or claims by third parties for any injury to any person or damage to property caused by Tenant’s pet.Landlord reserves the right to revoke permission to keep the pet should Tenant break this agreement or provide false or misleading information.

Fast forward three months, police are arresting them for fraud and obtaining property by false pretenses.

Ignoring buried equity only creates false cash flow.