Re: Can you truly understand budo without training in Japan?
Actually, it's my understanding that pizza is something that Italians now make for other Italians because it was imported from America and re-imagined for the Italian market. An Italian pizza is rather different from an American pizza.
Alex, I think you offer a valuable perspective re the marketing of Aikido. If Aikido or the Aikikai really wanted to be a marketing organization, there are lots of models out there which would be much more successful than your typical Aikido dojo. Just visit your local Tae Kwon Do outlet for an example. If Aikido has been adapted (or "simplified" or "dumbed down") for easy dissemination to a wider audience, it's still attempted to maintain some integrity as a martial *art*.
As for invented traditions, there are some videos available of O-Sensei warming up a group before a practice (see the Aikido Journal series of 5 DVDs), which are shocking to modern eyes. There is the Founder, running through his exercises--and half the group is doing something totally different, almost nobody is keeping time with him, the whole thing seems pretty much random. It's a problem to fetishize traditions, perhaps, but requiring people to sit up and pay attention does not seem so much of an ask.
As for O-Sensei's mystical vein, remember that the man evolved. He himself talked about re-envisioning Aikido in the wake of Japan's defeat in the war--and not just Japan's defeat, but in consideration of Japan's role and actions in that war. When you quote him, you have to think about when the quote came from. I'm sure he did mean exactly that Takeda Sokaku opened his eyes to "true budo." I'm also sure his idea of "true budo" expanded over time.