To me it appears that he didn't sit on it at first, but then changed his mind and sat down. I'm convinced that what you saw as him falling onto it is because he sat on it and then the legs buckled. The buckling caused him to fall further back, because the legs were stronger when they were straight.
The museum is mad that they left after that, but honestly I'd be pretty terrified going up to them and mentioning that I'd fallen into a priceless artifact and broken it. In theory, they didn't put up glass, and as professionals knew that means there's a risk accidents could happen. In practice, maybe they're short on funds and whatever bureaucrat sees suing me as a way out.
Not even a chair frame, but likely a wire frame, probably covered in foil and then crystals. That’s a common method for art pieces. This wasn’t a chair covered in crystals, but a ‘delicate internal structure’ in a chair shape.
e: that’s probably also why it was fairly easy to fix: re-bend the wire, then replace any crystals that fell of. This idiot is lucky he didn’t get a stabilising rod up his proverbial.