Observational studies linking diet to illnesses are, at best, flawed. Usually, an observational study works this way: a sample group of people are asked to fill out a questionnaire which prompts them to remember what they have eaten and in what quantities over a past arbitrary time period. (This is usually filled with memory mistakes- try and precisely tell me how many 3.5-ounce serving of lean red meat you have had over the past 30 days)
Then, researchers let some time go buy (it could be years) and observe who of these people develop the disease they are interested in. They then try to find a correlation between what these people reported as their diet a few years back, and the illness they developed.
It is very difficult to isolate single variables (for example, if you find that people who ate 20+ servings of red meat per month have a 7% increase in atherosclerosis, how can you be certain that the red meat is causing it and not the carbohydrates, alcohol, or poor exercise regime which usually accompany it?)
May I introduce the second most common type of research which tries to inform us on the way humans work: mouse-model studies!