Once the story is written it goes into “development.” This is when a Producer and Development Executives work with the Writer to get the story in rock solid shape, making sure the story works and will translate to screen.
When a Director is attached, she will also get a chance to make changes to the script. This is the first job of a Director – making the story better (yes, it can always get better).
A Director is usually hired because she has a sensibility – a particular perspective that will bring the script to life, so it might not always be the case, but often a Director will have a chance to give notes to the Writer and help them shape the story for success.
It is not the Director’s job to rewrite the script, but it is the Director’s job to give feedback that will help the script translate visually on screen and have the right emotional impact. Sometimes a Director will be asked to “make a pass” on the script, in which case the Director does, indeed, rewrite the script.