(Might be going off topic a little here, but I had an aha moment)
So The Hero Shade is a manifestation of OoT Link's regrets about not becoming famous? So, to make up for it, that is why he trains Link in TP? Makes sense.
"A Spirit Like that of The Hero's" is how I take it. The hero's shade and TP Link can't both have SS Link's Spirit, and I still feel as though it can be taken figuratively