Do cross trainer burn that much calories?

You burn fat because your body is running at a calorie deficit, not because you are exercising. What I mean is you can choose to eat less, or choose to add more activity. Either one (or a combination) helps create a deficit.

Eating less gives you a far more consistent deficit for weight loss because calorie burn estimates are much harder to measure than intake. I exercise because I want to be fit.

If cardiovascular exercise expends energy about your normal metabolic rate, it will cause your body to consume more calories than if you were at rest. In that sense, exercise "burns" calories, which may but do not necessarily come from fat. That's why MFP adds calories to your daily diet if you exercise. However, if you do not maintain a calorie deficit, including any additional calories you consume through exercise, you will not lose weight. It is somewhat difficult to measure calories consumed in exercise. I would not trust any number that you read off an exercise machine. It's better to measure your heart rate and use any of the various online calculators which take into account your gender, age and weight, to estimate calorie expenditure. To be safe, you might reduce that number, say by half, before entering into your daily calorie budget.