In the later '80s I was a member of the Canadian Airborne Regiment, we had our "fat bodies", but the vast majority of us were very fit. The Canadian Forces brought in the BMI as a fitness indicator, the idea being that those whose BMI was over 25 would be forced to do remedial PT. 75% of the Regiment had BMIs over 25. It eventually became apparent to the "Chairborne Commandos" of National Defence Headquarters that something was wrong (with the BMI, NOT the soldiers of the Airborne Regiment!) The problem is that muscle is denser than fat, and therefore weighs more per cubic inch. A very fit individual of the same height and general appearance as an unfit individual will weigh more, and thus have a higher BMI. The BMI was eventually dropped in the Canadian Forces as a fitness indicator.
The BMI remains a somewhat useful indication of POSSIBLE weight problems, but it's not an accurate diagnostic tool.