Is this in addition to the submethods mentioned in Apocalypse 6, which seem to solve the same sort of issues?
Yes. Submethods are for private implementation of a public interface. They're really ordinary public methods that just
happen to say "Don't inherit from me, keep looking up the tree for a real method."
By contrast, a private method cannot be called from outside the class. It is, in fact, just a subroutine that the class
declares with a syntax resembling method declaration, and that it can call with a syntax resembling ordinary method call, but there's no dispatcher behind the scenes trying to decide which class to dispatch to. It absolutely calls into the current class. If you use the ordinary dot instead, it absolutely goes to the ordinary dispatcher, which totally ignores all private methods, even in your own class.