Eating all your calories, not exercise calories

I believe those are calories that you are allotted based on hunger that you might have from working out or necessary food you might need to properly rebuild muscle. If you feel like you need them eat them, but if you're body tells you it isn't hungry then don't.

The calories that it adds on isn't about hunger issues at all. It's the amount of calories that you've burned during a workout. The reason people say to eat them back, or atleast half is because you need them.

Calories=energy. If you don't give your body the energy to work correctly then you'll be running on fumes hungry or not hungry. Your body will then want to hold onto everything you're eating (because it's technically afraid you won't replenish it) and not want to use the food as a way to function properly.

Actually hunger is directly related to how many calories you ingest. Yes MFP gives you numbers based on your information namely workouts that you do. Your brain is essentially running the same system inside of your body. A hunger pang is one of the ways that your body has to tell you that it needs more fuel or that it is "running on fumes" as you said.

There is no better way to know that you are not eating enough than your own body and the "hungry feeling is one of the primary ways provided by your brain. If you reach the calorie goal that they set for you before your extra calories from working out are added you certainly will not enter starvation mode. It takes more than not eating your MFP workout calories for your body to feel it is starving. As I said before it's calories you might need for you're body to rebuild itself after working hard but if you're in tune with your own body, and it wants more feed it. If not...don't.