Fujimura was the owner of Sarashina, a famous soba restaurant in Tokyo that dates back to the late 18th century. I don't believe he ever published anything in English, so Soba Technique is likely Udesky's translation of the title of one of Fujimura's Japanese books.

Anyway, neither Udesky nor Fujimura are/were historians, and I think they oversell the link between soba and beriberi (or rather, they're repeating a fairly common story that oversells the link).

The reason I feel confident in making that assertion (despite being unable to find any serious sources discussing the relationship between soba and beriberi in the Edo period) is that beriberi remained a serious health issue in Japan until World War II, killing thousands to tens of thousands of people a year. It was particularly an issue for the Japanese military since enlisted personnel primarily ate white rice and bread. There were 27,800 deaths during the Russo-Japanese War due to beriberi, for example (making up 34% of all Japanese deaths).

If there had been a well-established popular link between soba and beriberi prevention, we would expect efforts to have been made to address the prevalence of beriberi on that basis.

Instead, the first Japanese known to have made the connection between diet and beriberi was the admiral Takaki Kanehiro in the 1880s (this had nothing to do with soba, incidentally; he discovered it after investigating the difference in incidences of beriberi between enlisted personnel and officers). He successfully convinced the navy to feed its sailors a mixture of barley and rice rather than white rice, but this change only lasted for five years before being rescinded. The diet was unpopular and Takaki's theory was rejected by the Japanese medical community, who were convinced that beriberi was an infectious disease and that poor nutrition was only a secondary factor.