Another method would just be relying on the physical agility tests to tell the story. You have plenty of people who are "normal" that can hardly do a push-up, but plenty of "overweight" individuals who, as you sited, can do far more.

If someone passes all the endurance and strength tests with flying colors, why should their weights matter at all? Some people have naturally broad, stocky frames, and can still be in perfect health. My brother practices mixed martial arts and is a carpenter, he weighs 210 pounds and is 5'9". By the BMI, he's grossly overweight, but I'd dare any doctor to look at his daily regimen and nutrition and tell me he's unhealthy.