No question you will get some omega 3s/6s from animal products, but
from the animals of 100 years ago, even if you ate quite a bit of meat,
it would not be enough to displace the Mead acid in your cells (with
arachidonic acid), and this is a major factor in "chronic disease."
The other is free radical damage, which can occur with any diet, for
example, by how you cook the meat, and the lack of antioxidants in the
diet.
There were reports of the "Amish diet" a couple of months ago, and it
was found that they also had low rates of "chronic disease." Do you
think their diets contain more than 4-5% omega 6 PUFAs (this seems be
the dangerous threshold amount)? They don't use the highly refined,
high omega 6 oils. Stay away from these oils, don't cook food
containing cholesterol while exposed to air, don't eat anything that
has a rancid taste, and eat some foods that have decent antioxidant
content, but little or no anti-nutritive qualities (like non-fermented
legumes), and you will go a long way toward avoiding all the "chronic
diseases."