How do you define unreliable? BMI suffers from the same type I/type II errors as any other measure. For more information see this Examine article on BMI. BMI has a Low sensitivity and high specificity with regards to testing for body fat.
The short of it is if your BMI indicates you are obese, you are most likely obese, however an indication that you are in the "normal range" doesn't mean you aren't also obese. Obviously, there are outliers, such as very professional athletes, but if you know you are already quite fit and 'obese', then you aren't going to be testing your health or body fat using BMI, you've probably already done a few DEXA scans, numerous cardio stress tests and are in a camp somewhere.
For beginners, BMI is a fine metric (even at an individual level) and saying otherwise is a reckless misuse of statistics.
I'm just going to straight up quote the conclusion from the Examine article:
If you are normal weight or overweight according to BMI (18.5-29.9)
there is still a chance you are actually obese, and thus is primarily
due to low levels of lean mass (muscle, water, and glycogen).
If you are obese according to BMI, you are most likely obese
according to body fat percentage as well. When sampling from the
general population, over 95% of men and 99% of women identified as
obese by BMI were obese via body fat levels.
Outliers to this dataset, those who have enough lean mass to be
classified as obese by BMI but not by body fat percentage, are far and
few in society. These persons would normally be highly active athletes
or dedicated 'weekend warriors', and it is unlikely sedentary persons
or those with infrequent exercise habits would be these outliers.