Now, why the JLS says so is because during the execution of your inner class implementation, it creates the objects on the heap.
Now if the inner class object has access to local variables of the method, the objects of the class may use them
even after the method has completed its execution, ie. when they don't reside on the stack.
But, if it is final, its value cannot be changed, so its OK to use the variable, since it will be constant.
Aniruddha a method local class has a copy of the final constants and parameters of the method. That's why it can access them. This is implemented internally by the compiler. You can read my blog to be more clear. The URL is in my signature