What "big game" is being referred to here? Going to Sri Lanka to claim asylum, which is facing accusations of grave human rights violations of its own, is the equivalent of being a Muslim and trying to seek refuge in present day Myanmar.
If she was an opportunist, she certainly would've chosen a Western country.
If she was an opportunist but was low on funds to cough up even a one way ticket to the West, she would've aimed for India. If nothing else, Pakistan has zero influence here and there would've been at least a single sympathetic ear willing to listen to her story out here.
The only reason that I can think of as to why she wound up in Sri Lanka is because she probably had reasons to believe that she was being monitored by Pakistani authorities.