If pain were specific to the extent of being merely bodily sensation, then yes, understanding would have no part in its reduction...but as one sees with this article.....http://en.wikipedia.org/wiki/Pain
..pain starts with sensation and then expands to include many other things.
I certainly am not stateing the senation removes with understanding, in our conventional sense of things, but looking over that one can see may things such as phantom pains psychological pains and on and on do not amount to only sensation.
My personal observation is that sensation is only sensation. MOre than that is much more of pain than the sensation. The sensation makes you sweat makes your heart rate increase and nothing more, as message of avoidance. . If you say that is what you feel when you feel pain in every manner and sort...then yes your pain will never be reduced by understanding. But if you study your pain I think you will find your pain is much much more than that.All the much much more may be removed.
As to karma....it is certainly as cut and dry as that, there can be no accidental and karmic things as for one the rational consideration of such a thing precludes it....Imagine some are karma and some are accident...then what place would be things to a being....one would have perhaps a karmic thing...say received a 1000 dollar bill as result from some good act of compassion giving to another this thing....then the wind comes along as accident and blows that bill away...the result on the individual how could we say that individual then be resulted upon by karma..accident it all would be.
And result of accident would be no result of karma at all....as if karma never happened at all.Then we could all do bad and good acts simply wait for a accident and then they be all resolved....no that is not so.
It is either all karma or all accident. As it is clearly not all accident it must be all karma. As not a thing exists that exists perceived by one who does not exchange with that thing....so also all is karma, as exchange is necessary for this thing to be perceived as well.
Karma as in universes and all the rest....the large amounts of individuals and their karmic predispostions present in certain patterns that are perceived in such ways in grand scale and variance by no means infers such things are not exercised on the equation of a karmic root.
To large for us to see as each cell in a body sees not the body but itself does not infer the body is not all cells composed.
"This order considers that progress can be achieved more rapidly during a single month of self-transformation through terrifying conditions in rough terrain and in "the abode of harmful forces" than through meditating for a period of three years in towns and monasteries"....Takpo Tashi Namgyal.