I don't know that they would have just made them without permission, especially not as they were selling BSA air rifles.
The Japanese approach to copying other countries products was (at least in the 1930's) to obtain the licensed manufacturing rights. A few examples that spring to mind are the Lewis Gun, Vickers aircraft machine gun, Harley Davidson motorcycle.

My thought is that they made them with BSA permission or licence, possibly due to trade restrictions, but I have no information to support this idea.

When you see John Knibbs, please ask if he knows the name of the Japanese company(ies) that imported the BSA's in 1928 (or at any other pre-war period) This would help in my research.