It's both a problem and not a problem. Classic India. In the South stranger rape is almost never heard of -- they keep it in the family.
In the North, you have a lot of the dying vestiges of a downtrodden patriarchal social class that's lashing out at their dying social status and significance -- not entire unlike the neo-racism of the American South and similar marginalized working class clans these days.
The good news is that rape in India has got an insane amount of attention, especially when compared to the likes of neighboring China or Thailand who have politically suppressed talking about it.
Not saying rape isn't a problem in India, but it is also one of the most self-aware nations in Asia for dealing with it. I cannot say that about many other neighbors. But what you don't hear in the media is that a woman can walk home in the dark along Bangalore's main MG Road without fear of being assaulted or raped as is typical in much of the world, including the U.S.
Like I said -- it's classic India: for everything you observe to be true, the equal and opposite also exists.
A woman seeking political asylum for fear of rape should be taken seriously. But that could be anything: internal family issues in the south, one of the last power gasp reactions of an underclass clan in the north, or even just knowing India has done a decent job of its own global rape awareness so there's likely more to be sympathetic to such a claim.