I think @Lensing has a good point, and I think there needs to be a distinction between a message you as reader/viewer project onto a work and a message that an artist is intending to express.
Since you brought up movies, I want to bring up the movie STALKER by Andrei Tarkovsky, a film in which the director himself has brought up multiple times is meaningless in regard to the idea that Tarkovsky likely never placed a 1:1 meaning onto anything in his films and often preferred if the audience found their own meaning. Yet, it is a deeply moving movie for those who connect to it that spawns continual debate over its overarching message - whether the importance of faith, freedom or a myriad of other things. Often, it simply boils down to whichever of the four characters in the movie a person happens to connect with. It's undeniable that Tarkovsky is a highly intentional filmmaker, possibly due to his background as a photographer. So, something must be going on here.
It is possible for a film like STALKER to still have a message that wasn't intended or expressed if it was simply evoked. It has been claimed that STALKER is nothing more than an exploration of humanity that neither affirms nor condemns any of its characters' philosophies. Yet, by the deliberately long, hypnotizing takes of the film, the movie becomes a mirror. The viewer loses themselves in the movie and see themselves reflected back.
I think the book the movie was based on, Roadside Picnic, is another great example of this. A capstone novel on the life work of Arkady and Boris Strugatsky it's arguable that the book was largely exploring the feeling of the soviet people about the collapse of the Soviet Union and what happens next. I think many readers are surprised by the ending because the brothers don't give an answer. In the only way I can describe the end without spoiling it, the book simply ends with a man desperately wishing for answers. Leaving, at least for me, a feeling of everything and nothing having happened over the course of the book.
I've never liked the philosophy that art of any sort 'needs' to mean something. Often, I find it leads to situations where the artists get so wrapped up in their own 'big ideas' that they forget their art. Why do we expect art to make sense when life seldomly does? I think a better philosophy is to intend your work to evoke something, whether a feeling, a message, whatever.
I've been very surprised about the things people take from my own work in my collection of shorts 'Letters from the Sleepless', but in the end, even if it wasn't quite what I may have originally intended - it still means I did my job.