As indicated by a previous post, Yoshio Nishina was indeed the top Japanese atomic physicist during the War years. Following a 1940 survey by Takeo Yasuda and Tatsusaburo Suzuki, the Riken scientific institute was given an Army contract to build the Bomb. Nishina was appointed head of the project.
Although his research was initially on a modest scale, Nishina nevertheless managed to produce 1) a working thermal diffusion separator, 2) a small uranium ore-processing plant, and 3) a small amount of uranium hexaflouride gas---the first step along the gas-diffusion separation route that was eventually so important to the United States. While Nishina's separator did not work well, its basic design laid the groundwork for the construction of five or six much larger (61 feet tall!) units produced by Sumitomo under Suzuki's guidance in 1944-45. There were also three other machines at Osaka University that were capable of separating U-235, one of which was the only mass spectrograph in Japan; while Wilcox calls these devices "separators", it is unclear whether they were in fact dedicated specifically to that purpose. The improved Nishina-Suzuki models were apparently not found by US investigators during the Occupation. Most likely they were either sent to Korea or sunk en route.
There is at least one US intelligence report indicating the presence of U-235 separators in Korea apart from the Sumitomo thermal diffusion machines. It is also known that Sumitomo designed a centrifuge-type separator, although whether it was built is unclear.
Assuming 1) the Sumitomo separators made it to Korea, 2) the existence of an unknown number of additional machines indigenous to Korea, 3) German technical assistance on a still-undetermined scale---remember that Germany tried at least three submarine cargo missions to Japan, all with the express purpose of sending top secret weapons technology to their allies, 4) possible Axis penetration of the Manhattan Project, and 5) documented Japanese weapon design, is an end of the war test bomb really all that inconceivable?
Remember, I am NOT saying the Japanese bomb was a practical weapon, assuming it existed as more than a design on paper. There is no evidence that more than one Japanese warhead was ever completed, and the only possible delivery system would have been a kamikaze submarine. Further, by that point, even one successful Japanese nuclear suicide mission would not have altered the course of the War. (Although it certainly WOULD have killed thousands of Americans, either aboard the Operation OLYMPIC invasion fleet or, more likely, in a west coast city such as San Francisco.)
I suspect that the Japanese weapon, if it really existed and if it was actually tested, was probably a "fizzle"---a partially successful detonation of comparitively low-grade HEU. This coincides with what I heard from a retired Vietnam-era US Army intelligence officer, who told me the test actually took place but that "It was a small one". However, even a "not very powerful " bomb (as the BBC story put it) would still have been a triumph of Japanese wartime R&D, and a potentially devestating weapon had it been mated to a true delivery system---for example, a Japanese copy of the German V-2. (V-2 technology was aboard U-234, the last of at least three German submarines that tried to reach Japan in the closing weeks of the war; did the others get through? If so, how much German weaponry made it to Japan?)
Unfortunately we may never know just how far the Japanese Korean effort got because of the Soviet occupation and the failures of American intelligence and policymaking at the very end of the War. But certainly we ought to take the notion of a Japanese bomb seriously, and certainly it is not impossible that they succeeded, even if it's not necessarily likely.