I don't think this is explicitly true - I think if you want to make sure that everyone is getting your story from your art, the story you want told, then you need words. Once you release art out into the world, it is out of your hands. What it means, what it signifies and represents are all up to the interpretation of the receiver. That's true of any kind of art: poetry, prose, music, visual art. In a sense, as an artist, one has to be a control freak, focusing on every minuscule detail,, but also be able to give all control away once a piece is presented to the world.Working 100% visually, you're can't tell a story in one image.
You can do it and I said how. You can take a picture that tells a story more powerful than a news article like the image of the Vietnamese girl crying on the road. But most of my point comes from going to art school, hearing people over explain things instead of letting them stand on their own. Whatever I have in my head when I make something is totally irrelevant and might even detract as the details may be less interesting than the uncertainty or someone's imagination. There's a whole field that tries to tease out artistic intentions and it's called art history. And it's pretty useless. For the most part images can't tell a story on their own without some context so the act of making visual art is entirely release and any pointy headed thoughts put into it are as valuable as what a stranger experiences. I really don't know what I'm saying at this point. I'm on my phone, watching a movie and about to step out to the gas station.
"There's a whole field that tries to tease out artistic intentions and it's called art history. And it's pretty useless." haha, I like this. For someone trying to create something very personal and emotive then I guess it becomes "useless" to look at history in art because it doesn't relate to what you are doing. I would however say that it's very important to look at how people have gone about expressing very personal experiences in history. They may not be about a schizophrenic woman that overflows a bath tub but they could give you a glimpse into how other people express intimate experiences.
Artists and art historians have a good natured beef. Some sculptors look down on painters in a half serious half joking way. Many artists look down on photography. It's just shop talk when we congregate to talk smack about other fields. My first sculpture professor had a joke, "Sculptors deal with art in three dimensions, painters in two dimensions. And art historians deal with art in one dimension."