I'm afraid I don't see it that way at all. This sort of thing is dealt with all the time in the rural US, but in the relative absence of big government public transportation systems, the school district will get the one girl to school by negotiating a year of discounted rides (bulk purchase) from a car or van service with some reimbursement from the state. No more parties need to be involved, making it fairly efficient.
Japan should be doing it that way, too. Train companies in Japan aren't small businesses with kindly old proprietors; they are VERY complex businesses enormously tangled in cross-company ownership (our system owns 40% of yours, yours owns 40% of ours), government ownership, heavy government regulation with negotiated compromises (you have to serve these needs or we won't let you share that track), heavy union obligations, negotiated right-of-way through communities (if you won't service this line, we won't let you stop at the main station), etc., etc.
After living in Japan for many years, I'm afraid this sounds to more like a situation where keeping the train running for one person, though extravagantly wasteful, probably solved multiple practical problems simultaneously (fulfilling union employment agreements, rural service agreements, etc.) along with perhaps the greatest benefit: getting things done in Japanese bureaucracies requires so much negotiation among so many parties that just continuing to do what you have been doing (just keep running the train) is just SO much easier than changing the system--the system has so much inertia--that just letting it go on a couple of years longer was probably the easy way. The fact that it wasn't close to the cheapest way wouldn't necessarily matter to governments, unions, corporate managers and others spending Other People's Money.
I'm not implying anything about Japanese kindness. The Japanese do very kind things all the time, but this doesn't seem like one of them. I don't think kindness has much to do with it, because a private car service would be just as kind as making her stand alone twice a day on a freezing Hokkaido train platform and dramatically cheaper.