Depends on the infraction I suppose. I wouldn't expect such elaborate apology if somebody was just apologizing for e.g. bumping into me on the train. But yes, for a really heartfelt apology, I agree.

The idea is that people hear one of those languages as more "genuine" than the others, and are more likely to accept the apology, or believe the sincerity of it, if that language is spoken. I can follow the idea in theory, but am not sure I agree with in in practice.