Louie makes two claims. One claim is that for virtually all people, more chromium and manganese is bad. Quite plausible. But he also makes a much stronger claim that these and selenium, molybdenum, and iodine (?!) are not part of natural biochemistry, and so there is no such thing as deficiency. Even if we cannot identify the particular pathways where they go, it is easy to study deficiency in animals. Humans might have different biochemistry, but the prior is that it's all the same. Manganese and selenium deficiency are common diseases of sheep, thus subject to extensive study. They cause clear deleterious effects of commercial import. Farmers routinely replicate the experiment by treating only part of their herd, to confirm the diagnosis. Molybdenum deficiency is much rarer. Chromium deficiency is only observed in artificial environments, and Louie cites a paper disputing previous experiments inducing it.

Edit: actually, maybe manganese deficiency is pretty rare in livestock, though it does happen. But induced deficiency has clear effects, like miscarriage.