This quote makes absolute sense to me. Editing is just that.
When Michelangelo chips away the marble that hides the beautiful piece of art inside, so too do the editors cut away the clips. They cut and trim, transition and grade. Revealing the finished film that was always there, just hard to see with all of the garbage suffocating it.
A good editor can see the finished cinematic piece. They can see it as plainly as though it was being played on a 20ft screen before them. What makes a great editor though, is if they can show others what he himself can see.
To do that he must expose the greatness that lies beneath the rubbish. Because the line between the two almost always gets confused. If there is even the smallest amount of rubbish left behind with the greatness, well thats when it becomes an exceptionally average film.
An exceptionally remarkable film is made with precision.
He must be precise. Down to the very last frame.