That 20 year claim on the package is completely false unfortunately.

FEAR False expectations appearing real

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

Yes I know some people do it all the time and nothing comes from it, but it only takes one false accusation to do great damage. 

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. 

Also, false or misleading information on a rental application is also a solid reason for denial.

The landlord might not have known either, but he can't be sued for signing the lease under "false pretenses" because it contains a warranty of safety clause (it's also state law).

I'm assuming (maybe falsely) the odds are good that many who actually apply will meet the lease requirements (aka tenant checks) so then it's a matter of which one.