LL's need to collect ID and they can't have separate rules - like a requiring a certain type of ID for one person and not require any ID for another renter. That's how you get around that.
We run prosepctive tenants through a network at their expense(around $20/adult) and it requires a ssn#. It includes a credit check, and cross check for landlord complaints and they also check the provided references and report back; the service even checks for court actions against an individual (additional cost applies); If tenant does not agree to and pay for the screening, the application is terminated.
If something pops up on the standard check, the landlord reserves the right to opt for the additional criminal check for the additional fee (not sure how much it is).