The key word is 'pretty close'. Firstly, if what I read is correct, it only impacted the mediterranean basin, whereas bronze age civilizations existed in China, India, and the Americas as well.

As the article you linked points out, Egyptian and Greek civilizations were affected, but apparently there were other strong civilizations that were doing exceedingly well at the time at the expense of Egypt and Greece.

That's my point. Certainly, from any one perspective, societies can collapse, but that's just a localized problem. Never have we seen humanity suddenly thrust wholesale into some fantastical dark age.