Unfortunately looking "normal" could well be overweight. There will be a localised factor to what "normal" is too. I can understand why denial happens. I can only guess that the "sad face in the newspaper" approach is people wanting to vindicate that all is well with the child and that nasty NHS with its statistics is wrong. There are genuinely outliers... but most people seem to think their child is the outlier. Then there's the claims like "built like a rugby player" when a primary school age child can't have the required muscle development to rival a rugby player. Sadly too many slightly chunky baby faced reception class children end up looking like rugby players who spend too much time on the injury bench and in the club house by the time they get to secondary school.
Clothes are a poor guide. My DCs are the low end of normal range (like DH and I both were as children) and they look thin compared to many. Their clothes hang off them. Either the shoulders sag off/ trousers fall down, or I resist moving them up for length and the clothes get short. I've just had to retire 12-18 month shorts from DS1 who is nearly 8, not for the waist, but because the length is getting too 70s footballer. Usually he wears around age 4 for the waist. He weighs about the same as the child in the article but is 16cm taller.
Society likes the chunky baby/toddler phase and has lost sight of the fact that around 3-4, children should be looking lean through infant and junior school. By the time a child looks overweight by adult measures (love handles, moobs, double chins) they are considerably more overweight than you'd think.
We also over value the health benfits of structured exercise. It is a good thing, but not enough to rely on and replace traditional playing out and walking/ running around.
There does need to be better direct targeting of families to help them see and tackle the problem.