If you count bone marrow, brain, organ meats, blood, etc. an animal is pretty high fat.
EDIT: I'm also not sure about this western culture bias you're talking about, I am italian and we eat innards, blood and marrow. I am fairly sure every culture in europe does.
You can find hearts, livers, kidneys and stomachs, but except for chicken livers, pretty much only in halal (i.e. middle easterner) butchers, as far as I can tell.
Edit: Most English also tend to find blood saussages disturbing. There's black pudding, a blood sausage they make oop north, in Yorkshire, but people under the north-south divide won't go near it with a ten-foot pole.
And you should just see the expressions of disgust towards haggis (a Scottish dish made with innards and quaker oats).
When? Only in the last 10,000 years of agriculture, I guarantee you hunter gatherers did not get the bulk of their calories from plants. Also, it's heavily dependent on what culture you're talking about. Some cultures relied heavily on animals, others on plants.
