The BBC report on this study added the following disclaimer - which I think says it all - the study was utter rubbish.
The BBC says
However, there are limitations to the study.
The findings show observational associations rather than cause-and-effect and what people ate was based on self-reported data, which might not be accurate.
And the authors acknowledge that since diets were measured only at the start of the trial and six years later, dietary patterns could have changed over the subsequent 19 years.
Prof Tom Sanders, professor emeritus of nutrition and dietetics at King's College London, also pointed out that the use of a food questionnaire in the study led to people underestimating the calories and fat they had eaten.
"One explanation for the finding in this and the other US studies is that it may reflect the higher risk of death in the overweight/obese, who may fall into two popular diet camps - those favouring a high-meat/low-carbohydrate diet and those favouring a low-fat/high-carbohydrate diet," he added.