>It is good for predicting in general populations, but can easily fall apart with individuals.

While it can "easily fall apart with individuals", the difficulty lies in finding an individual to measure that will make BMI fall apart.

And that's because the huge majority of us is of the kind of complexion and body type where BMI works well.

So, sure it can give false positives, but for a quite small fraction -- besides any other rough medical heuristic does the same (e.g. signs of having the flu can also be caused by 200 other reasons).