Well, no need to take offense, I hope. I think myself the only point about Fuji is that in English Fujiyama is not "wrong", though it evidently is clearly so in Japanese. I've only heard it ever as Mount Fuji or Fujiyama. Fujisan I don't think would make sense to most American speakers.
Presumably the farther apart the languages, the less one country is going to pay attention to the niceties of the place-name nomenclature of another.
The Brits and Yanks and the other anglophones write France and Paris as the Frogs do, but the grenouilles write Angleterre, Grand Bretagne, and Londres, and nobody says it's wrong.....and these countries are close, linguistically and culturally.
Perhaps the idea is that translation of Japanese place names has proceded with misunderstandings and miscalculations. No doubt. But to suggest that the editors should have considered changing Jack's Fujiyama to something else is clearly wrong as an editorial matter.
This thread for some reason put me in mind of a thing that used to gripe me a few years ago: public radio commentators during the various Central American troubles of the time giving a distinctly Spanish intonation to Spanish words: Nee-ha-rahwa for Nicaragua, etc. Some of this still goes on. The use of a foreign intonation for the place names of foreign lands is a pure affectation. This is distinct from the use of a "spanish english" pronunciation as in American English; ie, La Hoya for La Jolla, etc.
Speaking of which; do the Brits still say Don Joo-an and Don Kwik-sote?