The calculator isn't 'wrong', it's just doing a calculation - what you then use that for...
Like it says
"This is general advice for adults only. It does not apply to children. It does not apply to pregnant women or breastfeeding women. Also your BMI may not be accurate if you are a weight-trainer or an athlete, if you are over the age of 60 or you have a long-term health condition. "
I'm of slim build, always have been all my life.
A few years ago we moved house and changed doctors, they'd only accept us if we booked-in with the nurse for a checkover - blood pressure, etc.
She measured my weight (clothed, shoes off) and height (the measure fitted above the scales so she had to dedust the height of them...) and worked-out my BMI was 24.something.
"oh you're nearly overweight", she said, "you'll have to start watching what you eat".
Hmmm.
A month or two later, a guy in the running club organised for a group of us to be guinea-pigs for the local college sports science course.
The students ran us though all sorts of tests, including body-fat measurement at 7 points using callipers - I was 15.something%
Obviously w-a-a-y fat.
See this site, which also does the calculation
http://www.menscience.com/Fight-Your-Bulge-with-Brains-_ep_106.html#
It cautions however
"The BMI formula is not without its faults, though. Because it doesn’t take into account bone or muscle mass, it may not represent a reasonable estimate for very muscular or big-boned men, or older men who may be classified as underweight due to low muscle mass. After all, according to BMI standards, the following celebrities are considered overweight: Tom Cruise (BMI 26), George Clooney (BMI 29), Mark McGuire (BMI 30) and President George W. Bush (BMI 26). And surprisingly, Arnold Schwarzenegger (BMI 33), Sylvester Stallone (BMI 34) and Dwayne “The Rock” Johnson (BMI 33) are all considered obese! For men with a great deal of muscle mass, it’s best to consult a doctor about their ideal weight, instead of solely relying on BMI calculations."