GameOnline, a Japanese game news site, reveals a bit more on this surprising revelation. Apparently, as the original Final Fantasy IV Super Famicom release happened on 7/19/1991, the song being included in textbooks appeared before those using it will have been born. There have, however, been a couple of FFIV remakes, in 1997 for the PlayStation and in 2002 for the Wonder Swan, so perhaps a few students will be familiar with the theme.
If anything, this should point to how much Final Fantasy has permeated Japanese society. Who knows, perhaps music listed as "from the hit videogame Grand Theft Auto" will one day be forced upon students in American elementary schools.