If obesity is a disease of poverty, then how come truly poor people (e.g., the poor in India or China) are skinny?
Lack of money for food is not a cause of obesity. If your goal is to obtain 2500 calories (assuming that is what you need to maintain a healthy weight) for a little money as possible, you will consume 2500 calories of carbs. You will not become obese. If you instead consume 3500 calories and become obese, you are wasting money on 1000 extra calories. You are not constrained by cost. You could instead reduce consumption by 1000 calories, and spend the money on increasing the quality of the remaining 2500 calories.
There is no significant research that shows adding exercise to an overweight person's lifestyle will significantly reduce their weight - typically just increases their appetite.
Increasing exercise and holding consumption constant will reduce body fat. One of many studies:
http://www.duke.cardiologydomain.com/images/uploaded/dukeh/2...
Do a google scholar search. The only difficulty is that you'll find so many studies which measure additional benefits to exercise that some of the studies measuring only effect on body fat will be buried. (I.e., the majority of the articles have conclusions like "exercise reduces body fat AND increases muscle mass", "exercise reduces body fat AND breast cancer", etc).
I'm curious, did you hear this claim from Gary Taubes? The one time I read a blog post by him, I discovered him to be incredibly dishonest: http://crazybear.posterous.com/how-1-graph-reveals-what-3000...