1. it depends on the writer. if he was hired by the producer to write
a formulaic script, he's a hack. the true 'author' of most films is
genre expectations, audience demand, and producer's financial-centric
guidelines.  most hollywood movies are made by poll numbers and box
office. LOR is tolkien pared down to CGI videogame effects.  if the
writer was hired by the director to fine-tune a script, the writer is
not THE author of the movie.

2. there are more than one layer of 'writing' in a movie. there is the
initial story and concept which could based on hearsay, newspaper
article, book--novel, biography, etc.  for example, some movies credit
story to one person while writing credits go to another which is like
an autobiography written with the help of a professinal writer.
then there is the layer of writing where the script is finished. this
begats the screenplay. but, everything that comes afterwards is also
part of the writing. writing for film is more than characterization
and dialogue. writing includes visual conceptualization and planning.
for example, in a novel, the writing isn't only dialogue but also
descriptions of place or mood or weather.  oftentimes, a screenplay
will only offer barebones story and dialogue. it's the director who
has to find the proper visual language to fatten it with flesh. for
example, the use of CU, zoom, pan, crane shot, editing, etc. are all
part of the language of cinema and expression. it's part of the
writing.  the reason why so many great novelists or playwrights make
poor filmmakers is because they don't have a grasp of filmmaking
language. they know how to write dialogue and characters but not how
to write with images, a talent closer to music, fine art, and
architecture.
a truly complete screenplay should be based on the finished movie and
describe in detail every aspect of the film--use of color, light and
dark, camera movement, editing, use of sound, etc--because they are
all part of the expression of film, usually ordered and guided by the
director.  similarly, verdi's otello is much more than shakespeare's
play. the musical performance is the real language of opera, and verdi
was the main author, not shakespeare.
lady from shanghai is a great movie because welles was the author.
yes, it's based on some cheap pulp novel, but the movie's greatness is
not the result of the conventional noirish twists and dialogue but
welles's visual expansion--filmic writing--on the original source.
if lady from shanghai had been directed by some hollywood hack, it
would have been just another forgettable crime thriller.
even when based on great material, the director makes all the
difference. campion's portrait of a lady is painfully bad.  house of
mirth is great.  lean's great expections is a classic. the ethan hawke
version is godawful.
welles' magnificent ambersons is magnificent.  arau's version based on
welles' very script is piss poor. writer or original conceptualist
deserves more credit than he deserves but director is almost always
the key. mario puzo said as much when he compared coppola's godfather
with cimino's sicilian. sicilian is clearly the better book but
godfather the movie is a classic whereas cimino's sicilian is
embarassing.

3. sometimes the line between writer and director isn't clear. there
are of course writer-directors like bergman and antonioni who are
comparable to singersongwriters like dylan. there are also creative
partners where writing/directing is blurred as with the coen brothers,
wachowski brothers, kaufman & jonze.

4. the debate is often really about auteur ideal than auteur theory.
should the director have the primary position in the making of movies?
 in the reality of hollywood genre movies, this is NOT so.  but
cinephiles want personal art which requires a vision and artistic
style and personality.  like bill buckley once said, mona lisa could
not have been created with everyone getting one dab at it.