No, I wish it were that simple. The comments about "one fly" really do mean one pattern that he (and some other tenkara masters in Japan) fish with to the exclusion of all other patterns. It has kind of gotten blown out of proportion, I believe. Amano-san does fish with just one fly. Every fly in his box is identical. Dr. Ishigaki has different flies in his box (same basic pattern, but different colored bodies and different colored hackles, plus he carries some flies that other people give him - I don't know if he fishes them, but if you look in his box you'll see them. There are other tenkara anglers in Japan do not limit themselves to one fly or one pattern or even what we think of as tenkara flies (including beadheads and dries).
Some people here talk about finding their "one fly" as if it were a vision quest or something. Dr. Ishigaki ran out of his favorite fly, bought a different one in a fly shop and found out that it worked just as well. He then decided that patterns don't matter and settled on a fly that was particularly easy to tie. That's how he "discovered" his one fly. The whole point isn't that you find your own one best fly, it is that the fly you choose doesn't matter. Pick a hare's ear soft hackle - you'll do as well with it as anything else. If you want something easier to tie, a Partridge and Orange. It will work most of the time in most places, so why worry about carrying two patterns?
Apparently it is universal in Japan that tenkara is a method of fishing only one fly on the line at a time, but that is not at all what the "one fly" commentary is about.