I would also suggest making sure that the criminal background check comes back clean, since the screening recommendation states that it is only based on credit.

I notice that most of the examples of references "saving" someone from making a bad decision on a tenant involve instances in which the problem would have been detected with a simple background, criminal, or credit check.  

Criminal background: No violent felonies within the last 7 years.

You can reject a Section 8 applicant for the same reasons you reject other applicants: credit score, Landlord reference (or lack thereof), criminal history, etc.