I am curious - the source for your "understanding" is?
Most of my "understanding" comes from a book called "The History of the Fender Bass". I'm at my office now and don't have access to it, but it led me to do more research online and all that info is still out there (see links below).
I called it a "different company" because it was never wholly owned by Fender (as most would assume). Since 1982, Fender USA has been the primary OEM customer of Fender Japan - a legally separate company from Fender USA. Fender Japan contracted the manufacturing to Fujigen early on, then expanded to include other factories in the 90s. MIJ applies to anything made at Fujigen - with it's heydey from 1985-1994 (?) - while CIJ applies to parts or models that are contracted out to other factories.
It's a fairly widely known fact that the Japanese were building exceptional knockoffs at the same time as US quality was going into the tank. The director of Fender (under CBS at the time, 1982) visited several of the factories doing knockoffs with the intent of sourcing their own Japanese made instruments to compete with them. He was so impressed with the factory that was doing the high quality Greco models (Fujigen Gakki), that they came to arrange a joint venture whereby Fujigen would produce "Fender Japan" instruments and their local partners would be their 2 main distributors; Yamano Music and Kanda Shokai,. Fender owned 38% of the original company, but details aren't clear on the legalities of the relationship after the CBS sale. It appears that the "Fender Japan" of today (and likely since 85) is owned by Yamano Music and Kanda Shokai, who handle their domestic market as well as the contract manufacturing relationship with Fender USA.
When CBS decided to bail on Fender in 84, Yamano loaned money to the group that bought Fender out from under CBS and when FMIC was founded in 1985, it couldn't possibly have owned Fender Japan since money was borrowed
from Yamano to buy the rights to the name, the patents, etc... It's likely that part of the "deal" to the 1985 investors included some sort of lifetime brand/licensing arrangement that allows Fender Japan to do what it does in terms of custom models and such as long as the USA market was out-of-bounds.
Yamano to this day still owns a piece of FMIC and its director was inducted into the Fender HOF the same year James Jamerson was.
http://www.music-trade.co.jp/Fenderjapanserial.html
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http://www.guitaristsource.com/guitars/fender-history.shtml#cbsYears
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http://en.wikipedia.org/wiki/Fender_Japan