Depends on how fat were talking, If your just 10-30 pounds overweight, what you said could be true. If your extremely overweight its impossible. Being in that condition just puts too much strain on your body, and most likely you'll be dead b4 50.There are plenty of 'fat' people who have no health problems what so ever and live healthy lives (in terms of both eating and exercising and what I mentioned above).
As for the BMI, you have to take that with a grain of salt, because just a pound or two can put you in the overweight category. Your friend probably just made the overweight category by a hair, but it doesn't mean their fat. A good doctor wouldn't tell you, you are.I also don't believe in this so called BMI system. If my friend is skinnier than me and was classified as 'over-weight' their must be something wrong with it xD