This is the latest from the American Red Cross concerning the background check issue. I have a confirmation from our ARC Chapter Solutions person (Diane Green) that the "exception clause" listed in the example below applies to Amateur Radio under ARES..
"Additionally, the American Red Cross often works side by side with partner organizations. Example: A church in a disaster prone area may partner with the American Red Cross to serve as a shelter for local residents during a disaster. If the church members are supervised by their own leadership, the church would set their own standards for volunteer screening and background checks. However, if the church members go through Red Cross training and offer to work under the supervision and management of Red Cross supervisors in a Red Cross shelter, they will be asked to register as a volunteer and submit for a Red Cross background check."
Follow this link for the full text of the American Red Cross statement concerning their required background checks.