BMI alternative for identifying obesity ‘could prevent misdiagnosis in millions’
(www.theguardian.com)
I could be wrong but your wording suggests you're misreading that.
Article states false positive rate is 3% and false negative is 5-9%
That's obviously not the same as wrong 3% of the time.
If we assume even tails then 8-12% of the time BMI incorrectly diagnoses.
Which is about what I'd expect. BMI is an approximate fit model, the further you get from the mean the less useful it is. If you are more than 1 standard deviation from the height mean you are much more likely to get a false positive (if you're short) or false negative (if you're tall).
In other words it's a line of best fit that doesn't work for outliers