Had it been an indigenous struggle, why would the divine (dus = ek) raiders be arrested by these very Kashmiri people in 65? This insurgency is a proxy war that was initiated by Pakistan and at that time even the US looked away as the bed was warm on the Afganistan experience.
After 1971 fiasco in which Pakistan shot itself in the foot by thinking that violence can be a solution in Bangladesh, there has been an itch in the supremist sort ideology of the Pakistani Army to foment trouble in India with an intention to undermine the integrity of India. First there was an attempt in exploiting the fluid situation in Punjab and after the USSR debacle in Afganistan the same mujahiddin were sent to Kashmir to foment violence and trouble.
Over the years, Pakistan has taken a lot of pride in the actions of these terrorists and in fact there was an attempt to glorify the matter with Kargil which is another Quixotic tale, I think best left for another discussion.
However over the years, as Pakistan has been exposed as the modern institution where occured the reniassance of current day terrorism, particularly since 26/11, the zeal with which the Pakistan establishment cheered for these terrorists has been ebbing. But clearly not finished yet.....
You can dump everything at Pakistan's doorstep but sooner than later this Kashmir issue with all its indigenous ill-will is bound to come knocking.