But most anti-cholesterol diets lower animal fat intake, not dietary cholesterol intake. Is this supposed not to work?

I had high cholesterol for years, I didn't take it very seriously because I'm otherwise healthy and I was eating healthy, but when I decided to take care of it I got it from around 210mg/dL to something like 140mg/dL just by changing all my meat/cheese to low fat alternatives as my doctor said. I am a big eater though, so maybe it doesn't make as much a difference for people that don't eat so much.