The real danger is not fat, even saturated/trans-fats, but starches and sugar. The increase in these types of carbohydrates in products like baby formula is actually leading to obesity in infants!
Excess sugar can stress arteries and damage them. Cholesterol is carried to these artier by lipids (LDLs and HDLs, which are not actually cholesterol, but proteins that carry it through your bloodstream). If you eat a lot of sugar, cholesterol can build up between the walls of arteries as they fix the damage. They can eventually break down the wall, releasing plaque into the bloodstream and potentially causing heart complications.
I highly recommend Dr. Lustig's video (UCTV) to learn more:
https://www.youtube.com/watch?v=dBnniua6-oM
A few years back I switched to a keto normal fat/very low carb (excluding fiber) diet. I've lost weight, gained energy and have felt a lot better. Of course this isn't for everyone. Some people have a body type that lends itself to higher carb intake (I knew a runner who'd eat 30 bananas a week) and as always do your research, consult with your doctor, dietitian, etc. before drastic changes in your diet.
It's a common myth that Adkins died of his own diet. He didn't, and Reuters rededicated their column implying that he did. I honestly wonder if the obesity epidemic would have gone down today if the world didn't dismiss his ideas, or the ideas of many nutritionist for decades before him that made similar claims about the dangers of sugar.