I just gave them my American license, the "official translation" from JAF, and my passport. Didn't need to show any driving history. I think they simply inferred that I had lived in the US for the requisite period because my passport was issued four years prior to my entry to Japan, and I only had tourist stamps from various countries dated prior to that.
Yes, those people are pedantic. A friend of mine needed to get an international license. For this he needed to show the DMV his plane ticket. He only had a confirmation email so he showed them the email on his phone. The lady at the counter responded that she absolutely needed to have it on paper. My friend scrambled around trying to figure out how to get it on paper from his phone, before figuring out that he could fax the email to himself at the convenience store across the street (or something like that). He brought the paper back, the lady at the counter looked at it, then handed it back to him immediately saying "ok, I just needed to see it."
Incidentally, if you don't have the foreign residency, you can't convert your foreign license at all, so you have to go through the standard new driver procedure (i.e., either go to driving school, or get a learner's permit and come back later to take the very difficult full exam).