So I went away and actually did the (literature) research on this. It turns out the answer is a little more complicated than fat suppresses appetite and sugar doesn't.
Basically, what little we understand of appetite control points to three hormones: leptin, insulin and ghrelin (great name). Oversimplifying massively, insulin tells you not to eat when your blood sugar is high and to be hungry when your blood sugar is low; leptin tells you not to eat if your stored fat is high and to be hungry when it is too low; and ghrelin tells you not to eat if your stomach is full and to be hungry if your stomach is empty.
However, to complicate things further, firstly these hormones interact with each other such that, for instance, if your stored fat is high, you will be less sensitive to low blood sugar or an empty stomach. However, you also adjust your long term sensitivity to these hormone levels to make the average level become the baseline, so if you're fat for a sustained period, your sensitivity to leptin will decrease and therefore low blood sugar levels or an empty stomach will revert to causing normal levels of hunger.
What this means is that sustained consumption of high levels of either fats or sugars will lead to increased hunger levels and therefore obesity. This sounds like a no brainer, but note that it is a cumulative effect, in that increased resistance to these appetite suppressing hormones makes it more likely that your body will fool you into overeating, which will make it more likely that your resistance will increase.
Finally, to link it all back to the article, the mechanisms controlling our sensitivity to these hormones is still poorly understood and known to be affected by such things as sleep patterns, stress and illness. It's therefore not too much of a stretch to say that environmental factors are causing a long term decrease in sensitivity. It would been nice to have a bit more of this detailed information in the article though and a little less 'it's something to do with leptin but we're not sure what'.