The stand-on scales aren't the best electronic tools, it's better to use the ones that measure through from foot to hand while you're lying down. Some gyms use these and so do BUPA. However, the fat calipers can be more accurate in the hands of an experienced person. There are other ways to measure fitness though eg. step test for heart rate recovery time, sit ups for core strength, grip strength measurement, sit & reach for flexibility, VO2max. A good gym should be able to offer a selection but decide which aspect of fitness you want measured.
On the BMI front, if I were aiming for 18-19 I'd have no body fat because the weight would equal my current lean muscle mass! I had my fat content measured by calipers recently.