That's simply not true about skim milk. It has just as much protein and calcium as whole milk. Maybe you and your siblings would have been even healthier with skim, maybe not, but it's not possible to deduce anything from your experience.
The article talks about this, but the reason it's so easy to binge on snack foods like juice is because they don't make you feel full and so you continue eating. Similarly, you'll feel much fuller if you drink whole milk versus skim milk, which is great for children who can't control impulses very well.