I think that most people say that you have to say something (good Shabbos or whatever). The chumra was to actually daven Maariv, which solves the problem more than just saying “good Shabbos” or “Boruch m’kadesh HaShabbos”.
But again, I’m not sure that he meant it as a chumra (and not a chiyuv)- that is just my guess, since I don’t think that anyone else says that, and it would be the obvious solution to the problem.