There has been some coverage of the fact that PCA's Georgia plant had obtained a "superior" rating on an inspection by AIB, apparently required by Kellogg's. Read this fabulous post by Jim Prevor at Perishable Pundit on this topic.
When my company used to be an ingredient supplier we were required by several customers to be inspected by AIB International (then the American Institue of Baking). This was before my time, so I don't really know a lot about the effectiveness of private third-party food plant inspectors. Nevertheless, all kinds of pundits and bloggers, who know even less than I do, seem to be advocating for more extensive certification as part of the solution to improving food safety. Like many of the supposed solutions, this is no magic bullet.