The British were ahead on epidemology, as it says. John Snow's investigations of cholera are usually regarded as the start of the field. However, the German sphere was not devoid of it either - Ignaz Semmelweis, who came up with the importance of hygiene in preventing infections, for instance. The problem is that correlation is not causation, and they were well aware of that at the time. Particularly Semmelweis had difficulty answering questions about the mechanism behind his evidence, since it was prior to germ theory. Anyway; so epidemiology was more established in Britain, but was by no means a method exclusive to them.

The evidence wasn't always clear-cut; Even though that article portrays the HMS Suffolk experiment as a turning point, the effect of citrus on preventing scurvy was still doubted 80 years later, and not without reason. They did not know of Vitamin C (or the B Vitamins) until the 20th century. They did not know that lime contained less of it than lemons; in fact they thought that since limes were more acidic, they would have a higher concentration of whatever was giving the prophylactic effect. They were unaware that Vitamin C is destroyed by sunlight, heat, oxygen, microbes and the copper tubing they used. As a result, there were still contradictory accounts of the efficacy of lime juice.

The situation with Beriberi was not much different; evidence appeared contradictory, and although Takaki was correct in that it was a dietary issue (although not a carbohydrate surplus but vitamin deficiency), he did not settle the debate, it still continued afterwards. See e.g.:

Manson, Rost, Sambon: The Phophylaxis and Treatment of Beriberi Brit. Med. Journ. (1902), 2, 830,

Wright: The Cause, Course, Prevention, and Treatment of Beriberi , Pub. Health Pap. Rep. (1905) 31, 289,

Herzog: Studies in Beriberi , Phil. J. Science, (1906)

The latter summarizes Takaki's work, and also the reasons for the reservations about it:

Takagi, late surgeon-general of the Japanese navy, still adheres to the theory that kakke is due to an insufficient diet, particularly to one containing a large amount of rice. When he first studied the question of the etiology of beriberi, the ratio of beriberi patients in the Japanese naval force in 1883 was 231 per thousand. After the diet was changed, the number of kakke patients in this branch of the Japanese service diminished, so that in 1898 the ratio was only 0.87 per thousand. However, it has frequently been pointed out that during this period of time the number of kakke patients in Japan had also greatly diminished in districts and among bodies of men where such a radical change of diet had not taken place.

Where the article writes that Takaki "rejected Western doctors’ hypothesis", it makes a bit of a false implication - Western doctors had no single hypothesis at that time and nor did Japanese ones. e.g. Yamagiwa and Yamanouchi, Über das Wesen der Kakké, 1904 concludes (my translation):

Thus Kakke or Beriberi denotes an intoxication disease resulting from the consumption of boiled rice of a poorly preserved variety as the main source of nutrition, causing the contraction of finer arterial branches in the systemic and pulmonary circulation, again causing dilation and hypertrophy of the heart, local anemia of the skin, mucous membranes, peripheral nerves, skeletal muscles and kidneys, and finally regressive changes in the intrinsic organs and tissues.

The references to 'German empiricism' and lab work might be a reference to the 1890s experiments of Eijkman (who was Dutch), who tried feeding chickens polished vs unpolished rice and showed beriberi-like symptoms in the polished-rice group. Eijkman's original inclination was to believe there was a toxin in polished rice though, not a nutritional deficiency.

It wasn't until the 1920s you had Hopkins and Funk &co coming up with the concept of vitamins and the discoveries of the actual compounds finally put the debate to rest, not just about beriberi but also about scurvy. (Eijkman's beriberi experiments lead to the discovery of an animal model for scurvy in 1907, when they tried using guinea pigs instead of birds)

Even if one took Takaki's observations as valid, they did not necessarily refute Eijkman's original idea that it was a toxin in polished rice, since his diet involved reducing the amount of it. It didn't refute the idea supported by Wright and others that it was bacterial, either, since diet could affect your propensity to contract an infection.

This article is painting many dichotomies with a broad brush; East vs West, British vs German, epidemiology vs experiment, Takaki vs the establishment. The perennial problem with these kinds of narratives is that they highlight the evidence that favored the correct theory while ignoring the evidence speaking against it, since we now know with the benefit of hindsight, that that evidence was wrong.

That makes it always seem so obvious that our hero was correct, that everyone else must've been plain close-minded, unable to admit mistakes, bigoted and so on. But when you go deeper, it's usually not the case. Even the losing side often had good arguments. At any given moment the frontiers of knowledge are all messy, confusing and often contradictory. No single theory fits all observations. So it becomes a matter of figuring out which evidence should be discarded. The article says 'it was plain to see'.. but was it?