I don't think BX is really legal for a chain hung fixture
You're right. 30-406(1) specifies stranded conductors. I missed that.
As to the tywraps, I was told that they aren't allowed, and I accepted it without checking. I'm going to follow up on this. However, tywraps holding BX aren't the mark of a quality installation, anyway.
When I read the definitions of pendant on the internet, I see the single drop point definition. I'm not in favour of narrow definitions, but you have a good point. Unless I'm missing something, I don't think it changes anything, here.
Thanks for the education.