A friend just got back from 6 months in Europe & was very clear that flying is a lot cheaper than trains. It also wouldn't surprise me if trains in Europe are heavily subsidized. So using trains as a competing example probably isn't the best idea. And finding a good example period is extremely difficult because almost all forms of transportation everywhere in the world are subsidized by the government.
You may be right; I think the actual rails are subsidized and only the trains that run on them are privately owned, so maybe not a good example. As for being more expensive than flying, for long distance (5+ hour drive), maybe, but I remember a trip from Rome to Netuno Italy (about an hour) was ~$16 round trip, and from London to Cambridge (about two hours) was ~$30 round trip. Both trains were local, traveling at about 80 to 100mph, while here in east USA, our Acella Express (US version of high speed train) only has a top speed of about 120mph, and costs about three times as much, despite also being subsidized.
I don't know what the situation is like in Japan, so even though they are also well known for their trains, I didn't bother bringing them up.