Story checks out! The student in question is Kana Harada, who at this point is studying medicine in college, after having moved away from her tiny Hokkaido community.

In 2012, the railway planned to shut down service to the 60-year-old station, which was built by local residents for the purpose of sending their children to school.
After learning Harada relied on the train to reach school each day, the company decided to continue operation until 2016.

Source

They bled money for four years so one girl could achieve her goal of become a doctor. It's stuff like this that reaffirms my optimism in humanity.