Perhaps, it is a cliche. Most of the non- vegetarians know it. Nonetheless, I will state the facts. The skin of poultry/chicken contains the bulk of their fat. Chicken contains around 20 to 25% fat. But the meat itself is only 7% fat. It invariably means that most of the fat of chicken is just under the skin.
It is easy, however, to separate chicken fat from their meat. Remove the skin. Contrarily, beef and pork is streaked with fats throughout their bodies. For this reason, nutritionists prefer chicken (less fat) over beef and pork.
Moreover, white meat contains less fat than dark meats. Domestic birds, however, have higher fat content than wild birds. Likewise, young birds are leaner than older ones.
Moral of the story–eat the bird. Not the skin.