This is a common misconception. BMI while an ok population metric, for individual's the biggest problem with is its poor sensitivity - it fails to classify people as obese who are obese.

Using your 6 3" male as an example, they are significantly more likely to be clinically obese (using waist circumference, body fat % etc) at a weight lower than BMI cut-off of 240 lbs.

It only fails to classify people with excess body fat who are in the healthy weight range.

It's really good at catching people who are obese who are overweight.