You are absolutely right. Reversing the roll in the "source" side doesn't eliminate the appearance of the arrows. It merely places them on the other edge (but same side) of the backing paper. On Kodak film (and Fuji, apparently) there are arrows on both edges. If one loads the film backwards, the *short* arrow lines up with the arrow on the film back; done correctly, the long arrow lines up.
Sorry for my topological silliness -- a little thought (or experimentation) would have solved the problem.