Do you require your non profits to provide documentation to show they are exempt from tax reporting? Or does checking the box on the signature card with the certification "I certify under penalties of perjury, etc." suffice?

Non-profits are not exempt from tax reporting. They still have to file a form 990. Certification of their TIN is not relevant. I believe that all non-profits are required to register with the SOS in most every State and you should be able to confirm their non-profit status.