Java static methods accessing private variables

You seem to be confusing visibility with scope. The instance variables are in the scope of an instance, so they cannot be accessed in a static method directly, but only with an instance reference qualifier: s._privateString in your case.

However, this does not mean that instance variables are not visible for a static method inside the same class, as private means visible inside the class (for any member with any scope).

Private member variables of class A can be accessed (i.e. read/written to) by any method of class A (static or non-static), so in your example, since the method changing the string is a method of the same class the member belongs to, it is granted access to the variable.

The reason is because a class is considered a self-contained body of logic (i.e. a specific implementation), so it makes sense that privacy is contained within a class; there is no reason to exclude static methods from that access right, since they are also part of the specific implementation the class provides.