The sample dataset explicitly excluded 'athletes', so would exclude people that _are_ outrunning a bad diet. We know that a little weekly jog around the park doesn't mean you can eat a cheesecake every day, but anyone who has done extensive 'athletic' physical activity knows that if you don't up your calorie intake that you will lose weight. The study does not conclude, at all, that you cannot outrun a bad diet. Instead, it suggests "that dietary intake plays a far greater role than reduced energy expenditure in obesity related to economic development."
Edit: My point is specifically not about running. I am merely pointing out that if you read the study you will find that it is more of a study on economic development, and not really useful for personal or localised health advice. It observes that economically developed population groups may be more sedentary, but do not expend significantly more energy - so a hunter-gatherer picking berries all day does not burn significantly more energy than an office worker (at least not enough to explain why the office worker is obese). Therefore, the link between economic development and obesity is likely related to food (dietary intake) than daily activity.