I suspect the only real link between them is 'Portia' browsing through Book Country to look for likely victims. I'm not that thrilled with Book Country (YADS yawn), but I don't think it's in the same class as LitFire and ASI.
Companies like the latter are always looking for new venues to find unsuspecting writers. Every book festival in my region will have a booth for ASI or PublishAmerica/America Star, as well as smaller vanity pubs. They try to work their way into genre conventions, and local writers' workshops and community college writing programs. They haunt twitter pitch sessions to 'invite' mms subs. They game open-nomination polls and contests with their authors' work, for use in future 'industry validation posts'.
But they're not actually - usually - affiliated directly with any of these.