If you don't feel like reading the article, there's really only a few sentences you need to read:
"This discovery made it possible to develop a precise hypothesis for how CO2 makes us fatter: We breathe more CO2, which makes our blood more acidic; this affects our brain, so we want to eat more."
“If you’re out running, you get your blood circulating and you can pump much of the CO2 out of your body, so our hypothesis is really further evidence that exercise is healthy. And exercise may be even more necessary in the future, when we can expect even higher CO2 concentrations in the atmosphere.”
Hersoug adds that fruit and vegetables also reduce the blood’s pH value, so the CO2 theory is also an argument for eating more healthily."
As far as I can tell, there's not really going to be a way to disprove the hypothesis. It's a pretty useless hypothesis, though. And I think the idea that exercising results in CO2 release through higher blood circulation is simply wrong. I think it's possible that exercising can result in greater CO2 release, but via increasing pulse rate seems ridiculous to me. For example, my pulse rate is around 50 at rest, so say I spend an hour exercising with an average pulse rate of 160 (which would be a pretty intense hour, just for the example) and with all of my time not resting (walking, etc.) I have a pulse rate of 80 for a cumulative 4 hours of the day. This would make for 85,800 beats per day, roughly. A person who does not exercise at all and doesn't even get out of bed would only need a baseline pulse of 60 bpm throughout the day to have more beats than me. I'd even guess that the typical obese person has a pulse rate between 90 and 110. I realize that there's more to oxygen delivery and CO2 removal than simple beats per minute, but the idea that blood circulating is why exercising is good for you is pretty ridiculous in my opinion.
Ultimately, though, the hypothesis is useless because it doesn't really provide any remedies that we don't already use for better reasons (exercising and eating fruits/vegetables).