He says they have no prior evictions or criminal record.

How would they enforce the crime, don’t cops have better things to do like catch real criminals?

Credit, criminal and eviction, no matter who is vouching.

Criminally that would include jail time?

They know crazy, they know criminals, they know what to do.  

I did not run a background check (credit check, evictions record, criminal records check) before she moved in, and now I am regretting it. 

Since the Treasury Secretary said they looked at the fraud components of this program, I'm assuming there will be some sort of political litmus test as a part of this process.In regards to people overinflating numbers, this is a loan document and if they are lying, they are committing bank fraud, which I'm sure the criminals will be doing.

However, I do already have credit reports, bank account balances, criminal history, etc.  

This is especially true with the tenant friendly laws in Chicago and Cook County which the following pertains to:In your apartment advertisement, don't include any criminal background qualifications/exclusions. 

Background checks, that's the beauty of listing on FB is you can check out their FB profile & if they have a picture of themselves smoking a bong you can easily skip past that person; if all else fails I know a guy who's wife is a PI and she can run a background check on someone for me for like $20 (it doesn't hurt that she used to work for the state's Department of Criminal Investigation).