They get groped all the time on trains--so often that there has been talk of making train cars available just for women
Your info seems to be a bit out of date. For at least the past few years (during which I've spent time in Japan) there have been female-only cars during the morning and afternoon rush hours. The proportions of cars:people is such that in the ladies cars mostly everyone can sit down, while the rest of the cars are packed like sardines (very uncomfortable, especially if you're mildly claustrophobic, like myself). With all of the time I've spent on public transit in Japan, I've never heard of any chikan. Westerners like to talk about this like every woman gets groped every time she goes on a train...probably because they watch too much anime, which is not indicative of real life.
Japanese women are in a completely different situation than other western women--they're really more in the position of women in the 50s or even more similar to women prior to WW2, where they had a predefined role to perform and certainly were not at the same level as men.
This is also not quite as bad as it used to be, and certainly not to American pre-WWII levels. Career women are very much a fact in Japan these days, and while there is still quite a bit of discrimination against them, it's not as bad as the discrimination against foreigners (especially other Asians; Koreans and Filipinos are especially looked down upon). The worst discrimination, IMO, go to other Japanese; e.g. the Burakumin
Japan's problems mostly arise from the fact that because of their recent feudal roots they are in in effect if not in name still a "class" society, dragged unwillingly into an industrialized world. The majority of their human rights and anti-discrimination laws are on the books due to external pressures, and are rarely enforced. For example, while it is technically illegal to discriminate based on race, there is actually no penalty for the offence.
Of course, all of this is terribly impolite to talk about, and I apologize if I've offended anyone. I actually love Japan and the Japanese people and culture; they just still have a lot of catching up to do, which is made very difficult by their unique culture of conformity and obedience.