A friend of mine uses LoseIt and I saw how it does the eat-back. I think it does that because the base calories it was suggesting (for her at least) were very low, so you can afford to eat your exercise.
I did not eat back my calories when I was losing -- I usually burn about 500-600, 5x/week. To me that was key to my success. Now that I'm in maintenance I am eating them back because if I didn't, well, it would be maintenance.
What are you doing that burns 1000 calories? I have a polar HRM, too, and I'd have to run at least 10 miles to burn that much!