I think you are right to be upset.
When my DD had these tests last year, I thought all the people at her school refusing to let their children be weighed and measured were nuts. What's the harm, I thought?
DD then got a letter saying she was obese. She has been 25th centile for height and weight since birth. I went and had her weighed again at the doctor's, and she was 4cm shorter and 4.5kg lighter than they had her on the scales. It took me six weeks of calling the NHS to try to get this rectified. In the end, they clearly thought I was being a delusional parent but agreed to take her name off the register, and offered to come and weigh her again (apparently a GP's measurements weren't good enough - also they said they couldn't possibly have muddled her up with another child).
I was disgusted with the letter I got sent. I also then weighed and measured my three-year-old. She is 2nd centile for height, 9th for weight. She has always been tiny. But on the children's BMI scale on the NHS, even she is something like 70th for BMI. How can this be right? There's not that much of a discrepancy between 2nd and 9th centile that she could be 70th for BMI. The two scales don't match up.
Not only that, but BMI is notoriously inaccurate even for adults - it's just a guide - and more so for children, who may genuinely be heavy-boned, about to have a growth spurt, going through a 'puppy fat' stage, and nonetheless be entirely healthy.
After this experience, I think these tests are intrusive and unhelpful. Getting that letter made me feel like crap even though it was a mistake (and then fighting to have it acknowledged as a mistake, which never really happened, made it worse). And it was deeply patronising, offering to refer our entire family for help with healthy lifestyle choices with absolutely nothing to go on about our 'lifestyle choices' but one four-year-old's BMI. I think it could cause a lot more damage among some parents - how many children will be put on diets or told they are fat after getting a letter like this?
I totally get promoting healthy eating, making it easier for families to make healthy choices, and for schools to be healthy places. But to me this whole thing is a waste of time and money.