"Would you like to login using Facebook", that question that pops up on many non-Facebook sites, is so obvioualy a bad idea that most rational adults will click "no" 10,000 times, even without stories like the above. You really have no idea what Facebook is doing behind the scenes, but you sure don't want it to involve your authentication credentials for any other sites, or any other personal secrets for that matter.
Some will do it though, eg. children, perhaps young people or just the less cynical among us. Therein lies the problem.