When I see that quote, I assume that it is talking about a long newspaper article trying to describe a noteworthy person or event. So that is the thousand words that I think of.
For a photographer, a more appropriate question is to ask, "What picture?" Some pictures definitely don't tell a story, and aren't worth a thousand words. Imagine a photo of a gunfight. The answer to "What picture?" that could tell a thousand words would be a photo showing inconspicuously the town's name, some landscape that would show the locality, someone's expression showing how the hero was regarded, as well as someone's expression showing how the villain was also a human (like the sad face of his mother), and of course both of the prime characters in the gun fight--showing a story in each one, although not necessarily with their faces.
This is what makes photography so much a different art than videography. With video, you simply take a video of the event, and the story is told. Improving the story is a matter of improving the perspective and directing the event. With photography, it is completely different. In order to tell a story with a picture, it is not enough to simply take a picture of the story, but to put the parts of the story together in the picture. A low angle of a flock of baby ducks splashing water above themselves and quacking merrily would make a photograph that told a story. (This example comes from a recent photo situation I saw near a highway in my city.)
A photograph essentially requires the use of art in order to effectively tell its story. With a video, the story can be told even without the use of art. With the example of ducks above, a photograph of some yellow blobs several feet straight down out the window of your car on top of a one-dimensional spot of wetness on a service road to a freeway downtown would tell nothing. A video straight down out the window of your car of those same yellow blobs would still tell the story that they were ducks splashing in a puddle, but there would be no art involved. You can see the birds splashing in a video, regardless of the art involved. But a photograph to tell the story of the birds splashing requires greater artistic achievement. And to tell the full story of where the birds were downtown near the freeway would require a very beautiful touching photo. A video telling the same thing could be absolutely horrible, though, simply rotating the camera to the highway and then back.
The standards of art are far higher for telling a story with a photograph. And "What picture?" can tell a thousand words is a question that we as photographers make a life out of answering.