This study uses 24-hour dietary recall. Pretty much "What did you eat yesterday." Dietary recall studies are notoriously the least reliable method of measuring effects of diet on health or mortality. They will pretty much say whatever you want them to and are used mostly as filler for scholastic papers and headlines.
tldr: It's the quality of your diet that counts for mortality.
Yes, title is somewhat confusing because I read it as "low fat and low carb are associated with mortality", whereas the article treats of correlation with the reduction of mortality.
Didn't read closely, but they could be saying that macronutrient composition of diet is actually irrelevant to mortality. Rather, eating a high-quality diet (presumably lots of fresh vegetables, fruit, etc.) is actually what matters.