This is a great article. But something I wanna bring up....
In fact, I can't think of a single legitimate reason for double nested classes. If you find yourself writing one of these, you should probably rethink your architecture. If you find yourself doing this routinely, you may want to consider taking a long vacation.
Double nested classes are heavily used in JAXB generated classes. In fact every sub-element in an XML is automatically bound to a static inner class by JAXB. Since JAXB evolved later than when this article was published, I'd presume that the Author missed the usecase.