It's my understanding that what today is called the BMI is NOT BMI. My recollection is that BMI was developed as a more precise measurement of fitness than the height and weight tables. My first exposure to the concept was Dr. Kenneth Cooper's book and his explanation of how he measured it by immersing the patient in a tank of water. And I believe the point of this procedure was because it WASN'T POSSIBLE to determine a person's BMI from their height and weight. Over time, people looked for an easier way to approximate BMI without water immersion and "pinch" tests became common (the fat fold on the stomach, back, or arm). Today they use height-weight tables to calculate BMI which makes absolutely no sense to my understanding and memory of the concept. Am I suffering from false memory syndrome?
You know much more of the science of this than I, evidently. The immersion you mention reminds me of how specific gravity is measured.
The opinions I have stated above are more from observations of the political consequences that result from what to me, were arbitrary changes in the criteria of obesity. I was looking more at the socio-political-economic side rather than the health side. The sudden "epidemic" of obesity was more manufactured than factual IMO.