I think there are two possibilities here. Either it's a bug or the documentation on PHP.net/manual is incorrect. Here are three sections of the PHP manual. First on inheritance:
Object Inheritance
Inheritance is a well-established
programming principle, and PHP makes
use of this principle in its object
model. This principle will affect the
way many classes and objects relate to
one another.
For example, when you extend a class,
the subclass inherits all of the
public and protected methods from the
parent class. Unless a class overrides
those methods, they will retain their
original functionality.
This is useful for defining and
abstracting functionality, and permits
the implementation of additional
functionality in similar objects
without the need to reimplement all of
the shared functionality.
And on abstract classes:
Class Abstraction
PHP 5 introduces abstract classes and methods. It is not allowed to create an instance
of a class that has been defined as abstract. Any class that contains at least one
abstract method must also be abstract. Methods defined as abstract simply declare the
method's signature they cannot define the implementation.
When inheriting from an abstract class, all methods marked abstract in the parent's
class declaration must be defined by the child; additionally, these methods must be
defined with the same (or a less restricted) visibility. For example, if the abstract
method is defined as protected, the function implementation must be defined as either
protected or public, but not private.
Finally, interfaces
Object Interfaces
Object interfaces allow you to create code which specifies which methods a class must
implement, without having to define how these methods are handled.
Interfaces are defined using the interface keyword, in the same way as a standard class,
but without any of the methods having their contents defined.
All methods declared in an interface must be public, this is the nature of an interface.
Suffice it to say: there is nothing in the documentation that mentions inheritance of private methods. If there is a relationship between the parent and child method signatures, then it is not documented and the bug report should at least show someone that the documentation needs to be updated (if the decision to have this behavior is intentional). And if there was not supposed to be a relationship, then well, it's a real bug.
That's my opinion...