I think that is a horrible write up. Fat is consumed as the length of exercise increases. Intensity will decrease of necessity as the length (endurance) increases. Obviously, you cannot run two miles at the same pace you would use for a 100 yard dash.
Exercising with less intensity intentionally, however, simply decreases the calories burned.
If you are over twenty minutes, you are burning fat stores.
If you are over twenty minutes with greater intensity, then you will burn more fat stores than at a lower intensity.
Keeping your heart rate low has absolutely NO BENEFIT in burning extra fat. That is the most idiotic thing I have ever read in my life. It makes no sense whatsoever. You will burn less, not more, as you decrease the intensity.
The only reason to lower the intensity is if you cannot keep it up for more than twenty minutes. In that case, lower the intensity, but increase it progressively as you get into better shape, and your workouts will become more effective over time.
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Here, fuel sources.
http://www.humankinetics.com/excerpts/excerpts/the-bodyrsquos-fuel-sources
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For what it's worth, at least he got the 20 minutes correct.