There is no single number that perfectly represents body fat percentage without a lab-grade method like DEXA or hydrostatic weighing. Everything available outside a lab -- BMI, the Navy tape method, skinfold calipers, smart scales -- is an estimate built on a formula, and each formula makes different assumptions about how body shape relates to fat.
Why BMI isn't a body fat number at all
BMI only uses height and weight. It was never designed to estimate body fat percentage directly -- it is a population screening ratio that correlates with fat levels on average, across large groups. Two people with the same BMI can have very different body fat percentages depending on muscle mass, which is why athletes routinely get flagged as 'overweight' by BMI alone.
How the Navy method tries to do better
The Navy tape method (used by the U.S. Navy for fitness standards) estimates body fat from a small set of circumference measurements -- neck and waist for men, plus hips for women -- combined with height. It accounts for body shape in a way BMI cannot, which generally makes it a closer estimate of actual fat percentage than BMI alone, though it still has known error margins and can be thrown off by measurement technique or unusual body proportions.
Skinfold calipers measure fat thickness directly at several body sites and can be more accurate still, but only in trained hands -- inconsistent pinch technique introduces more error than the Navy method's simpler tape measurements.
Using these numbers sensibly
For most people, the practical answer is: use the Navy method or a body fat calculator for a rough estimate, use BMI as a quick screening number, and treat your own trend over weeks and months as more meaningful than any single reading. A DEXA scan or hydrostatic test is the only way to get a genuinely precise number, and it is rarely necessary outside clinical or athletic contexts.