Yes, to play fast one must play...fast. But there`s a thing called "fast degradation". So, I think we must begin a piece playing slow, one or two bars or a musical phrase. Then, when we are abble to play these bars slowly but well - when they are "in" our fingers - we must try to play them fast and see if we can do it well or if there are speed walls. In this last case, we can eliminate speed walls with the PS, thumb over, etc. And return to play slowly. Slow - fast - slow...
Its very important play slow the last time we play the piece in the day. If we play fast the last time, in the next day we cant play well. And this is true when one go to the lesson with the teacher. The last time we play before going, we must play very slow, not fast. All this is very well explained by Mr. C. Chang.