I think that Emma Silversides explained this quite well on this thread.
The bit she said that was relevant was:
The second physiological result of endurance riding is that at a lower intensity, our bodies burn a higher percentage of fat as fuel (as opposed to glycogen, the stored form of carbohydrate). Thus the popular term “fat zone” or “fat-burning ride.” Don’t be misled by this though since, in reality, your body will burn more calories at a higher intensity level (although the percentage of fat as a contribution to fuel is lower). So relatively, you burn more fat at a higher intensity (since the caloric total is higher). But the key here is that our body’s first choice for fuel during higher intensity exercise is glycogen, and exercising at a lower intensity level helps your body become more efficient at burning fat for fuel.
Basically I think this says that you are right, it just explains why the term "fat burning" zone is used. I was always confused about it as well.