--We have not yet encountered a situation where our health department is listed as a research site as for a multisite study  subject to the revised common rule Single IRB requirements. OHRP allows exceptions to single IRB requirement to be made "where review by the proposed IRB is prohibited by a federal, tribal, or state law, regulation, or policy, or if there is a compelling justification for the exception. " Our DPH administrative rules state "The Director may require that proposals submitted to the Department that have been approved by another IRB be subject to review and approval of the Department's IRB", but given the OHRP guidance,   I am thinking our rules may need revision to  more closely align with the  OHRP verbiage re "prohibition". 
--With regards to training, our current plan is to continue to verify human subjects training for investigators who will be working with identifiable DPH data at the beginning of the study; but for continuing review/status update reports, we will require signed (by the PI) verification that human subjects training for all investigators is up to date, without requiring documentation. However, we will also inform the PI that training documentation is auditable-- ie verification of training must be provided upon request .