Low Rent Income Property - Screening Tenants

In the BP Tenant Screening book, there are two initial screening items that would cause a prospective tenant/applicant to be Denied, 1 - does not earn 3x the monthly rent, 2 - cannot get a qualified co-signer.  There are several other recommendations from posts, blogs, podcasts on BP that also have other indicators for denial, e.g. no past evictions, criminal activity, etc. 

But if we use just the first two as a path to denial, what is the success rate others have had in getting good tenants accepted for low rent property? We are looking at some opportunities in older (but safe) neighborhoods that will attract renters with low income and would like any input from the BP community to help guide how best to screen/accept these tenants who are likely to have some marks on their record.

Also, we have created a scoring system (thank you Michele Fisher http://www.biggerpockets.com/users/fischem)....but we have been told by a couple of landlords, that if we stick to our scoring, we'll never be able to rent to low income candidates, even though we've tried to keep it within reason.  Any thoughts would be very much appreciated.