If the board has authority under the HOA rules to enact a social media policy, then if a HOA member violates it, they can take whatever action they are allowed to take under the governing documents for HOA rules, etc. violations. The key is making sure that they actually have the power to enact them.If there is defamation, you can hold the poster liable (e.g. sue him or her). If the page administrator edited, modified, or otherwise contributed to the content, you could hold the administrator liable, too. But if the administrator does not participate in the post in some way but simply allows it on the page, he or she is not liable; you need to have him or her do something beyond simply maintaining the page for liability to attach (the same way that FaceBook is not liable for its members' posts, or a newspaper for comments in the letters to the editor).