When you pull up a skin fold between your thumb and fingers to measure with calipers, what you get is a folding of two layers: a skin layer and an underlying fat layer.

Think of it this way: 1. Lay out a thin green wash cloth. Fold it in half. The thickness of the fold is comprised of the thin green wash cloth. Open the green wash cloth out flat and top it with a thick red wash cloth. Now fold the two together so that the green is on the outside. The thickness of the fold is now comprised of the green and the red wash cloths. The thickness of the fold gives you a picture of how thick the red cloth is when both cloths are laid out flat. Consider the thin green to be skin and the thick red to be underlying fat.

Find a place on your body where you store no fat: the backs of your hands perhaps or maybe on the outside of your ankle. Pull up a skin fold and see how thick it is. This shows you what a pretty much fat-free skin fold looks like. Some people like to call this paper-thin but it is actually thicker than paper. Now pull up the skin folds in the areas you are refering to. If they are thicker than "paper-thin", there is a detectable fat layer beneath them. Watch over time as those detectable layers get thinner and thinner.

I hope this makes sense. In person, I could show you skin folds and I could draw a picture of the structure of skin and underlying fat but the wash cloth example was the best way I could think of to put it in words.