I think this one is overly obvious, but I think I really understood the value of this statement after doing my own film.
I must have heard it before from others, but the first time I actually do remember it entering my mind was when I was in my Sound Mixer's place doing the sound stuff for the film. It was such a great line... and very bittersweet as well.
As a visual person, I was obsessed with the look of the film. It was where I got the majority of the 'high' from. I just had to have it look really nice. But one thing I learned from this process, and from seeing many other films is that, once the first 10 seconds have passed, and the audience has 'acclimated' itself to the world and style of your film, the 'visual look' aspect of your film kind of disappears over their head and they get more immersed, and focused on, the STORY. That sorta becomes the end all be all that they are now really judging your film on. THAT IS, assuming you haven't done any drastic changes to the visual styles in between scenes that forces them out of the hypnosis that they are in. As long as the visual style stays generally consistent, I found that their attention shifts wholeheartedly to your story and how much you worked on the visuals doesn't become irrelevant, necessarily, but definitely drops in tiers, exponentially. If the film is sub par in story, but really well done in the visuals, it doesn't really stick in their minds post-film experience, I find.
This could also be a result that so many movies from Hollywood these days look 'polished' but lack so much substance.
So yeah, i really learned the value of knowing that you have a solid story that really resonates with people, and let the visuals supplement that, but visuals in itself cannot carry the film... unless you're doing some crazy abstract visual journey where these crazy changing visuals that are connected to the storytelling.
on a side note, but still related. check out Richard Willams' Thief and the Cobbler. The Uncut version. It is pretty incredible and very interesting visually!
Manu