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I can't tell you what is 'safe' for you.
However, I can explain the 'fat burn' range a little better.
When you workout, your body burns whatever fuel is most readily available. Usually this is Glycogen (which is released from your liver), but your body can also burn fat and muscle fiber.
If you are working hard enough, your body won't be able to run off glycogen alone, and will have to substitute one of it's backup fuels (fat or muscle). Fat provides more calories, but muscle fiber is more quickly accessed. If you work out too hard, your body won't be able to burn fat quickly enough to fuel it and will break down muscle fiber for energy (so you will end your workout with just as much fat and less muscle). If you go too slow, you will just use glycogen which will be replenished as soon as you eat something. In between, you will use mostly body fat for fuel, thus directly burning fat off your body.
Higher heartrates make for a stronger cardiovascular system, so the range above 'fat burn' is typically a good training range for improving your cardiovascular endurance and health.
Of course, this is a very simplistic answer, and you can burn fat by running hard also as it will boost your metabilism for a long period of time. Same with heavy weight training as your body will raise your metabolism to help heal itself.
Hope this helps,
Greg
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