One bad apple doesn't mean the whole bunch is rotten 
And it's not like Japan is the only place with perverts. Japan just has a more interesting story because it seems to happen exclusively on the trains.
It's far from just one bad apple, and these type of stories are often in the news.. I remember awhile back when 1 girl went to report being groped, and the police officer taking her report got busted for taking photos up her skirt from under the desk..

And it's not exclusively on trains either and happens quite a lot in the work place too.. A few years ago, it slightly happened to my wife.. This fucker didn't grope her, but he did pin her to a wall by her shoulders and confessed his love, which is more than enough to piss me off.. Took her to the local police station to report it, and the cop said they couldn't do anything, cause it would be "her say" against "his say".. They didn't even want to speak to him, so I took care of it myself.. Didn't punch him in the face or anything, but I bet he wishes I did, cause I totally fucked this guys life up.. Within a month, he lost his wife, 2 kids, house and job.. Guess I kinda fucked his whole family up, but I don't care!! Don't touch my bloody wife!!