Not only have I always wondered this, I’ve had my Japanese students asking me. However, only now got round to researching it. I did already know most of this Wikipedia entry:
“The word diet derives from Latin and was a common name for an assembly in medieval Germany. The Meiji constitution was largely based on the form of constitutional monarchy found in nineteenth century Prussia and the new Diet was modeled partly on the German Reichstag…”
but that still leaves open the question of whether foreign commentators invented the expressions (like “bullet train”) or if the Japanese people setting the Diet up chose the description of it in English (the Japanese expression “kokkai” always being used when speaking that language).
In either case, I wonder if they didn’t choose the word “parliament” because they didn’t want it to sound like a real parliament, given the powers of the Emperor and in the case of Westerners perhaps their unwillingness to accept that an Asian country could run a real democracy.