Eat More, Weigh less?

MFP incorporates a deficit regardless of whether or not you exercise. If you exercise, the calories you burn are "extra" and not necessary to lose weight (in theory). So that's why MFP says you can eat back those calories. Because even if you did, you'd still be at a deficit.

For example: If your TDEE (total daily energy expenditure) is 2200, then to lose weight you'd eat 1700 calories a day to lose 1 pound a week (or 1200 calories to lose 2 lbs a week). If you exercised and burned 200 calories, then your TDEE goes up to 2400. Thus to lose 1 pound a week, you could eat 1900 calories. That's why when you exercise you're allowed to eat more. This is what MFP does. Using the settings, you tell it what your TDEE is and it gives you what you should eat if you didn't do anything extra.

However. A lot of gym equipment and apps are VERY inaccurate when it comes to telling you how much you actually burned. Sometimes it's up to double! This is why you have to be VERY careful when eating back calories. Most people who eat back calories will eat back half of what they think they burned, just to have a buffer.

Hope that helps!

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