(1) You are responding to a quote about a proposed rewrite of the sentence which would be clearly wrong independent of whether the quoted text was (the “less correct” was chosen because the proposal asked if it would be “more correct”), and

(2) No, there's no such requirement for the use of “[sic]”; use for things which are not strictly incorrect but not comport to a stylistic preference of the author presenting the quote (or one that the author expects the audience to have) is common. For instance, Google's dictionary's usage example for it is “a story must hold a child's interest and “enrich his [sic] life.” What the “[sic]” flags is grammatically correct, though recently usually stylistically not-preferred.