Static members are independent, lets define independency here.
For static variables, the space for a static variable is not allocated inside the instance of class. ie if you create an object of a particular class with some static & non static variables, all non static variables will get space inside every instance, but static variables get space in the JVM memory outside the instance & has single presence. static variable will be same for all the instances of class.
For static methods, you can call them directly using the class name & you don't need an instance for calling. the "Function Activation Record" or stack frame creation for all the methods is same & never changes.
So basically the term "independant" means independent of the "instance" that you have or may create. Hope that answers...