As I understand, as per the new FB changes for brand pages (moving them to timeline structure), fans/members/likers are allowed to private message a \"Page\" or \"Brand\". I
Just last night, Facebook has just announced new APIs for managing Pages which include, among others, the ability read messages from a page, hiding a post etc.
Quotes from https://developers.facebook.com/docs/reference/api/page/ :
You can read the messages for a page by issuing an HTTP GET request to /PAGE_ID/conversations with a Page Access Token and read_mailbox permission.
Reply
Note that a page can only reply to a user's message. It cannot initiate a private message with a user. Also, a page can respond not more than twice to a user's message before the user has replied back.
You can reply to a user's message by issuing an HTTP POST to /CONVERSATION_ID/messages with the following parameters.