Here is one example, of several, I'm sure, where a friend class can be legitimately used without disregarding the reasons for encapsulation.
MyClass inherits from GeneralClass. MyClass has gotten big, so you created HelperClass to encapsulate some of the function of MyClass. However, HelperClass needs access to some protected functions in GeneralClass to properly perform it's function, so you make HelperClass a friend to MyClass.
This is better than exposing the protected functions, because they don't need to be available to everybody, but it helps keep your code organized in an OOP way to keep MyClass from getting too complex. It makes sense, because although HelperClass isn't concretely related to MyClass by inheritance, it does have some sort of logical connection to it, embodied in the code, and in design, as "friend".