The video you saw was porn. The only alternative would be that it was a gang rape recorded on someone's phone. That would keep it relatively short and it would be low quality. It's unlikely.
I've heard of one rape on a train. In Japan that is, I've heard of plenty more elsewhere.
The molester thing is more prevalent, but you're talking about trains that are so crowded you can barely breathe. You don't know whether the thing pressing against your butt is someone's hand, their groin, a bag, an unfortunate child's head, or anything else. Also if someone does get trapped with their hand pressing on your butt they can't move. Women sometimes accuse men of groping to get cash payments for silence. No-one knows exactly how prevalent groping is because of all the false accusations.
Anyway, every country has it's perverts and it's rapists, so it's not surprising that Japan has them too.