It’s kind of weird (if not confusing) for me to read that. I’ve never seen that “avoir beau X, Y” thing being used other than for the first case scenario you’ve talked about. And I don’t think it’s even right to use it that way (the second one). Could I have a little more contextualization over here?

In this specific sentence, X and Y ARE as usual in opposition if the person who wrote it sees ‘élevé dans une société martiale’ as brought up with a sense of honor. Honor and perfidie are in stark contrast.

My explanation is that Avoir beau X, Y is normally used here with a stark contrast between ‘honor’ and ‘perfidie.

Despite (X) having been brought up with a sense of honor,
he is surprisingly Y= (perfide).

What makes this specific sentence sound Strange is that when we hear ‘société martiale’, this doesn’t necesserily brings to our minds the idea of ‘honor’.