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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,...

I was under the impression that
извинить - из-вин-ить - to forgive, pardon
извиниться - из-вин-иться - to apologize (by extension of the idea "to excuse oneself")

As you say, that is in fact...