As Chris said in his earlier post, it depends upon which koryu art. Each school is different, sometimes very different, and have their own rules, regulations, and ideals. Getting an instructor's menkyo takes about 10 to 12 years of dedicated training in the two koryu that I am most familiar with. Many of the people currently running a koryu dojo do not have any certification since they have something that is more important in the koryu world. They have the permission of the hombu dojo. The koryu are all about continuity, and knowing there are others that can answer your questions as they've been doing it longer. This is how they've managed to survive all of these years. If someone says they are practicing koryu but they do not have a connection back to Japan, then they are not practicing koryu. As Chris pointed out, understanding Japanese culture is not as important as understanding historical Japanese culture, where the koryu came from. And this is only really important after a certain point in the training. Initially, no knowledge of Japan or the Japanese is needed to begin training. Eventually, you will run into things which make no sense unless you've got some understanding of the culture from which it came. Bowing properly is one of the things that westerners have the most trouble with.