Anything that sick people do less is inversely associated with mortality. The "controlling for blah blah blah" stuff can't be believed---are the researchers succeeding at controlling for everything that affects health? Not even close.
If you see a claim about food and health that doesn't spend a huge amount of time talking about the researchers' experimental or quasi-experimental approach, just ignore it.
If you see a claim about food and health that doesn't spend a huge amount of time talking about the researchers' experimental or quasi-experimental approach, just ignore it.