They can access non-static members of the enclosing class (including private non-static members) on an object of the enclosing class.
The operation "accessing" can be done in many different ways:
1) accessing a member variable by using it in a method of same class body, without an object qualifying the member variable.
2) accessing a member variable with a qualifying object. Eg:- myObject.myMemberVariable
3) ...and potentially a couple of more different ways.
The two authors you quoted meant different ways of access.