I feel this is best explained with a testcase:
This is the error DMD gives:
test.d(21): Error: arryacc(3LU) is not an lvalue
code: #####

class A {
   private size_t size = 5;
   auto newArrayAccessor(T)() {
      T[] a = new T[size];
      ref T accessor(size_t i) {
          return a[i];
      }
      return &accessor;
   }
}

void main() {
   uint[5] arry;
   ref uint acc(size_t i) {
       return arry[i];
   }
   acc(3) = 5; // works

   auto a = new A;
   auto arryacc = a.newArrayAccessor!(uint)();
   arryacc(3) = 5; // doesn't work. What gives?
}