Interesting article! I think I'm probably on the side of avoiding using извиняться now; the article points out the exact logical gap that was mildly worrying to me:
"... заявить: «Я, конечно, виноват, однако не нуждаюсь в вашем прощении»."

Though at the same time, the maxim "-ся indicates no more than simply: this verb will not have a direct object (will require preposition, or is intransitive)" seems like an okay rule, moving forward. Unless there are bountiful exceptions that are escaping me.

Makes me wonder, is раска́иваться, for instance "Я раскаиваюсь!", a possible alternative?