That's only true if you have the peculiar western idea that meat is just the lean muscle tissue of the animal.

If you count bone marrow, brain, organ meats, blood, etc. an animal is pretty high fat.

I have heard stories from my parents and grandparents that my great-grandparents from Germany would save all types of animal fat (Goose, Pork, Beef etc) and use it for cooking and soap making. It was a precious commodity and was not thrown away. Also I think butter was pretty available. It wasn't until WW2 I think that it became scarce and vegetable oils and margarine came on the scene.