It depends on a million things*, but that doesn't sound THAT far off what it suggests for me. FWIW, it has worked for me. If it's too aggressive for you, try slowing down the weight loss rate.
I find anecdotally that I can eat 1600 and burn 300, for a net of 1300, much easier and more comfortably than just eating 1300 and skipping the workout.
There is also more to it than straight calories; not all foods are created equal. Some are significantly more nutrient-dense and satiating for the same # of calories than others. You will feel more hungry if your calories tend to come from carbs, if you're cutting too far back on fat, not eating enough protein, etc.
*including but not limited to: your height/weight, muscle density, level of activity, metabolism rate, rate at which you would lose weight to reach your input target weight by your input target date, etc.
MFP estimates are really low for me. I used 1700 when I was losing weight and added back my exercise calories on top of that. I don't know your specific stats, but 1200 is way too low for me. Try putting in a higher activity level and slower target weight loss.
I'm kind of a small person, fairly fit and have a desk job working from home so sadly yes 1200 calories would be just about right for me to lose weight.