Why ST must make SS and PS coauthors is precisely what does not make sense in SS story. SSS is cited, and they could discuss how SSS should be cited. That would be the normal course of action. The papers addressed different questions.
One reason why SS has such agency is that he knows he is considered an RA on his other AERs. SSS is the one paper he could own after multiple papers on various economics of supermarkets. As SSS turns flaccid, he hasn't all that much to applaud left on his CV, and decides to rub himself and PS onto ST. SS is a careerist.