Actually you're wrong. The body needs a minimum of 1200 calories to maitain basic organ and bodily functions if you're a woman. When you exercise, you must eat 1200 plus whatever you exercise, as this means your deficit won't be under 1200.
Example: Exercise 500 calories at the gym, eat 1200 + 500 = eat 1700 calories to lose weight. You will still have the same calorie deficit to lose weight without putting your body through starvation misery, as the deficit on days that you exercise comes from the exercise rather than the cutting of calories from diet.
I am also on a 1200 calorie diet, I notice great results when I eat what I exercise. Eating back the calories doesn't defeat the purpose, consider it 'banking'. You don't eat them back and watch your metabolism slow.