I provided the other side a great hint which they failed to recognize. Here it is spelled out in great detail for them: A trained historian would be trying to access original documents like O Sensei's travel diary and his callendars. As well as those of the people around him. As well as any related receipts Etc. Only with these will you be able to establish how much he traveled during different periods and with whom.
This is what the people you are arguing with have done. YOU are the one that needs to do this. Quit treating the Dobson and Saotome books as scholarly works, they aren't.
When I was in college I had a history class that the ENTIRE grade was based on one paper that we had the whole term to write. It was simply to answer "Was Constantine a Christian?" We were only allowed to use primary sources from within 50 years of his death. It was incredibly difficult and really drove home the point of just how much room for interpretation there is behind a textbook statement like, "Constantine converted to Christianity in the year 312 AD." To the best of my ability, I have tried to apply that same critical thinking to how I view OSensei and what he was doing.