The fat burning zone is a bit of a popular misconception
At lower heart rates your body gets a greater percent of it's energy by burning fat. At higher heart rates a greater amount comes from other sources eg glycogen.
HOWEVER - at higher heart rates the TOTAL calorie burn is higher and you will actually burn more fat at higher heart rates
For example:
say at 140 bpm 75% of energy comes from fat - if you exercise for 40 minutes and burn 300 calories, 225 of these calories will be from fat.
at 160bpm maybe only 50% of energy comes from fat, but if you exercise for 40 minutes you might burn 500 calories and therefore 250 of these will be from fat.
so in the second example you are burning a greater total number of fat calories.
Two important things to note:
If you are just starting to exercise you need to work your way up to the higher intensity exercise, and so the lower heart rates are more appropriate.
I believe that some people stick to the lower intensities when cutting in order to protect lean tissue as much as possible.