Not only are you correct ...but the basic article is incorrect - in that the Japanese send their spent fuel to France for reprocessing!
Obviously, spent fuel has decay heat - and it might sit in a spent fuel pool for cooling for 5 to 10 years - and then is shipped off for reprocessing, but NO - not all spent fuel remains on-site (unlike our American reactors - where the federal government promised to support - reprocessing (then stopped by the idiot peanut farmer) - planned off-site fuel storage - Yucca Mountain - stopped by the present idiot who makes the idiot peanut farmer look competant!)
Note - go back and read some of the discussions during the initial time frame after the tsunami - there were discussions of the impact of Mixed Oxide (MOX)Fuels contributing to the problem. MOX fuels use reprocessed spent fuel...plutonium from spent fuel, maybe some “fresh” enriched Uranium so that the new fuel can provide power over an 18 to 24 month operational period before the next refueling.
Thanks for the details. I believe I read that the French waste stockpile is much, much less than ours, because of this.