Eating foods that contain saturated fats raises the level of cholesterol in your blood. High levels of LDL cholesterol in your blood increase your risk of heart disease and stroke.
Keep in mind that the source you cite runs contrary to millenia of human evolution prior to the rise of agriculture. ;-)
Here’s an opposing viewpoint:
http://www.nytimes.com/2002/07/07/magazine/what-if-it-s-all-been-a-big-fat-lie.html