But he is an athlete with almost no fat (he is not aiming at muscles so he does not have a diet that minimizes fat, he is looking for sheer power and explosivity (gym, martial arts)). He is very built up (muscular) though.

So I wonder how the BMI can give any kind of reasonable indication when the fat level is not taken into account.

Sure BMI can be more or less accurate depending on the person, but for those few who have actually rendered it inapplicable to them it's going to be blatantly obvious. No one will confuse them with being obese.

I wouldn’t have been obese before, but I technically am now (with reduced bodyfat %).