the trouble with this is interpretation.
On a primal/paleo diet, you can be low-fat. You simply have to eat more fruit and veg to be that way. As a poster as pointed out, it's entirely possible.
Trouble is, most people watching said news programs are not at all interested in their health to look beyond food guide pyramids and tv news spots about "health." Thus, they are eating a highly processed diet with a lot of transfats, chemicals, grains, and so on. My own ILs are on a "low fat" diet and have been for years (since a family member was diagnosed with heart disease in the 1970s). My SIL is a major low-fat advocate. They eat so much processed and junk food, but they are "right" of course, and we are both wrong and crazy.
The real, real trouble for folks comes in when they add "high fat" to this insanity of a highly processed diet. That causes a mess. And a lot of people do it, So cutting the fat (rather than processed) does help them.
Better would be to cut all processed, then find the macro-nutrient ratio that works for you. Might be zone in any one of three ways, right? Right.