They might be right, they might not.
There are lots of skinny/slender or light people with very high % body fat, usually caused by bad diet, lack of exercise and generally slobbing about. Look at supermodels for one, many of them have the body tone of a elastic band and are incredibly unhealthy.
On the flip side there are a lot of large/heavy people with very low % body fat, many rugby players, Chris Hoy and so on.
According to BMI, the first group are healthy, the second are obese.
Either way, the school has no way of detecting "internally stored fat" unless they send the kids off for lots of scans (expensive) and they shouldn't be delivering news of this type in this way.