You may also want to look into having criminal charges taken out against the tenant.

If I were to rent to them that would mean straying from my original perimeters set for tenants (good credit, 3X income, good rental history, no criminal background). 

She is betting that you are the kind of LL who pockets the application fee and rents without really running a credit/criminal/eviction check.

That means you either had 1. a loose key floating around, 2. a corrupt criminal with agent access who copied it, or 3.

If I run a credit/criminal/eviction report and an applicant does not check out, I do not return the fee.  

Do you have anything in your lease about criminal activity?

Yes we do, if they meet all of our rental criteria (residence/rental history, income/employment history, financial/credit history, legal/criminal history)  and with additional security deposit to cover our risk. 

just like your vetting a tenant.1. credit report 2. criminal back ground3. brief bio and track record.. if you have done deals copies of the HUDS when you bought when you sold proving your profitable.4. your market and why5. the specific deal.6. copies of bank accounts proving you have some money.

When we had it they were small time junkies/criminals.

Landlords in New York City who use illegal methods to force a tenant to move are also subject to both criminal and civil penalties.