Jason, It's against YP rules to have a closed Facebook group for BSA. I agree that it's silly, as long as parents are part of it, but a rule is a rule.
To help ensure that all communication on social media channels remains positive and safe, these channels must be public, and all communication on or through them must be public. This enables administrators to monitor all communication and help ensure there is no inappropriate communication between adult leaders and Scouts or between Scouts themselves. Therefore, no private channels (e.g., private Facebook groups or invite-only YouTube channels) are acceptable in helping to administer the Scouting program.