It's the ratio of plant protein to animal protein in the diet. So no you don't need to go hard vegan. But yes, it is the diet and there is hard evidence.
My personal question is, does a high fiber ketogenic diet (high fiber, high fat, low carb) raise or lower cancer risk? I don't know of strong evidence either way.
Nutrition seems difficult to study because there are so many biological mechanisms at play, but we can get a rough picture at the macro level.
Of course someone always blows findings out of proportion and decides to take things to an extreme.
Added: Schistosomiasis infection is such a huge cofounder for colorectal cancer rates that it is ridiculous to have claimed dietary cholesterol from animal sources as the cause.