One piece of evidence that flat discussions don't work well at all: on general news sites which have numbered flat comments, I often see comments that start with 'reply to number 4...'. Users are actively trying to make up for the lack of threads. Of course, such discussions quickly become unreadable.

The article points out some valid criticisms of threaded discussions (like excessive indentation), while ignoring the giant mess that flat discussions tend to become. The funny thing is that it's a false dichotomy. Even the article mentions the possibility of having just one level of reply, and yet in the last sentence it just reverts to 'Always favor simple, flat discussions instead.'