It shouldn't be a permissions issue if the bb is allowed to have anonymous access. If you think it's an access issue, then create a read only user in phpbb and use those credentials as the user initiating the search on the content source.
My belief is the issue is that all the posts and comments are stored in the phpbb database and are the root of the problem. Have you configured a crawl rule on this content source that includes the the option, Crawl complex URLs (URLs that contain a question mark (?)) (based on 2007 server central admin, I don't have access to a 2010 CA at the moment).