Actually, they are not disagreeing with nutrition science. They are disagreeing with nutritionalism. And they are right (although some of the specific links might be replacing one kind of nutrisionalism with another).

Here's the difference. Nutrition science IS science. It's results come from controlled, replicable experiments, checked via peer review and analyzed correctly for significance.

Nutritionism is the belief that food is just the sum of independent nutrients and other substances, and once we know what nutrients we need we and which substances are bad, we can rearrange and pick and choose to get an ideal diet, coupled with the belief that we know enough from nutrition science to actually understand enough of nutrients and other food substances to actually do this.

Nutritionism IS NOT science. It is to nutritional science what pop psychology is to neurobiology.

Here are some examples (based on real things, but I do not have specific references handy so I'm going to keep the details generic). Suppose nutrition science finds that substance X is vital to health, and that carrots are high in substance X, and that people who eat a couple servings of carrots a week get enough substance X.

Synthesizing substance X (or extracting it from carrots) and adding it to to some other food, and then telling people that they can use that other food as a source of substance X is nutritionalism, not nutrition science. Or making X pills for people and telling them these can supply the X they are not getting from their diet is nutritionist, not nutrition science.

This is because it is possible that in order for our digestive system to actually extract and absorb substance X, it needs something else (substance Y) which is found in carrots, but is not found in those supplements or in the food that the synthetic X is added to--and so people getting X in the supplement or additive form are not actually making it available to their bodies.

The X supplements do not move from nutritionalism until scientists actually do the experiments and show that we can incorporate X in that form, or gain sufficient understanding of the mechanism by which X is absorbed to be able to say it will work in supplement form.

Another example: for almost everything we are told we must eat more of (fish, carbohydrates) or less of (red meat, carbohydrates, fats, cholesterol), there exists some culture for which (1) their traditional diet goes massively against that advice, and (2) people who eat that diet are healthy.

That's because the advice we get in these areas is NOT based on nutrition science. It is based on nutritionalism. The science that says that, say, red meat is bad for you ACTUALLY says that in particular studies of particular populations, red meat was bad. For people that strongly match the characteristics of the populations in those studies (e.g., whose complete diet is similar to the complete diet of the participants, and who live similar lifestyles) the conclusion that they should avoid red meat is probably pretty accurate. Since there are other populations in which red meat consumption does not appear to lead to those bad health effects, however, the proper conclusion is that the dire effects of red meat cannot be generalized outside of populations like the study populations.

Your best bet if you want to avoid nutritionalism is to try to stick to proven traditional diets. If the people of some region or culture have been eating a certain way for hundreds of years, and are in good health, that's pretty damn good evidence that their diet as a whole works. If someone's theory says that they should be in poor health because their diet includes too much X, or doesn't have enough Y, then that someone's theory is incomplete or wrong. In science, when results and theory disagree, results win.