We've got the experts to help. As you point out, static member classes do deliver an organizational advantage. First, they help unclutter your packages. Second, they provide a convenient way to convey association.
Classes can employ static member classes to define their data-associated structures.
For example, a tree class could define its node interface as a static member class. However, static member classes provide other benefits. Therefore, a static member class has access to its containing class's static members, even private static members. Likewise, the containing class has access to its member class's members, even private members. Because static member classes operate just like any other members in a class, they follow the same access control rules and can have private, package, protected, or public access.