The point you are making about it being impossible is as moot as the one those that fear AI are making. From logical point of view, singularity (a moment when AI has modified itself to the point beyond our capacity of control or even understanding) seems possible. I don't see a way for us to tell what will happen when it hits.
One needs to remember that AI itself may not be evil, it just may exterminate the human race because it feels it is the right course of action at the time (i.e. there is no good and evil for the machine, at least not in the way we understand it). If it does not, it might solve all the problems of humanity. There's just no way to tell what will happen IMO.
Here's a link that I recommend checking out on AI:
https://news.ycombinator.com/item?id=8391896
It received little attention last time but to me it seems like a good piece.