For chimps, it depends largely on their environment. Chimps that consume large amounts of meat tend to be much larger than chimps who don't, indicating that they rely on meat for protein... I guess the figure is just large compared to other primates, who rarely eat any meat aside from the occasional insect.
For humans, a minimal of 50% plus of our daily calories were made up of meat during our hunter-gathering days...good article on marksdailyapple went through that and had a couple of nice studies. Guess that isn't a lot compared to what some people consume nowadays, but a lot of tribes were really successful with a diet that had a much higher concentration of meat (think Inuit). I know that there is only one successful indigenous tribe that consumes less than 60% of their diet from flesh now adays....forget the name of the tribe but will look into it.
As for the nutrient-dense diet of the tarahumara....don't really buy that. Land sucks down there for growing, and growing corn and beans does nothing but destroy topsoil, sucking the nutrients out of it. I guess it depends on who's calling it "nutrient-rich", and what their definition is. Last, I would probably agree that the cause of cholesterol is more important than the cholesterol level itself. However, the correlation is interesting and would be a good starting point for a study.