Innerclasses are defined within another class and they are like members of the enclosing class. So just like the members of a class can be private or protected too, innerclasses can also be private or protected, just like methods of a class(because they are members of the class) can use the private members of the class, that is why innerclasses can also access the private members of the class.
One reason for the behaviour shown by innerclasses is because they are members of the enclosing class.
OCPJP 6-100%; Preparing for GATE11
subject: Top level class Vs inner classes access specifiers