I used to work for a young, very switched on consultant in care of older people. He used to say that there was research that even if someone went from a diet of chips and fried mars bars to zero fat protein and salad, NO ONE could reduce their cholesterol by more than 2 points. People get mixed up between dietary fat and obesity. Sadly, because I am traditionally built, obesity does seem to result in higher LDL levels.
I don't know what research he was quoting or whether it has now been superseded, this was about 12 years ago.