I've heard this advice and have even given it myself over the years and I really want to apologize for doing so.
"Let the work speak for itself."
So let me be clear: No, don’t let it ever do that. The work speaks in a secret language only its creators understand. If you do, you are allowing the viewer's interpretations and biases speak for it instead. You have to provide context to allow people to see the work as intended.
Ideas are cheap and design proposals are fragile. Not until they are hammered and hardened by a robust design process are they able to stand on their own and take a beating and, even then, companies spend enormous amounts of money to make sure that their message is clearly communicated well before anyone gets their hands on the product. It's called marketing, public relations, and communications. Apple spends a billion dollars in marketing. Microsoft – over two and a half billion. Samsung – over four billion. Why won't they just let their work speak for themselves?
Our ideas have to go through a tremendous amount of development and iteration to become finished products. In the same way that we work on the product design, we must work on designing the communication so that the work is received in the best way possible and that you get the outcome you want. Unless you have the corporate influence to make decisions by yourself, you need to recruit people to your side. Very few of us have the genius to create work that stands on its own.
In college I majored in Art and minored in Design, so I spent a significant amount of time with dirty hands and paint-streaked pants. I learned a lot during those formative years; I remember having to write artist statements for our art shows. Sometimes these did a good job of framing the work and providing context, but just as often we earned the label of “bullshit artist”. It wasn't always a bad thing.
When we let the work speak for itself, the critiques showed amazing breadth. The various interpretations said as much about the critic as it did the work. I am reminded of this article on Vice called "I Don't 'Get' Art"; fair warning, some strong language and opinions up ahead.
There's clearly a range, but Art is different than design so this kind of open interpretation isn't necessarily helpful. Often, art is about making a statement, asking questions, being provocative, evoking emotion, showing human potential. Design must provide solutions, answers, and delight. The best products do quite a bit of both.
I'm not advocating just developing dazzling bullshitting skills (though they are quite helpful), but I do believe that good design needs good communication. This allows the work to be received in the way it was intended, and in the process removes barriers and recruits advocates to help it along.
Even our best work often can't stand on its own, especially during its infancy. It needs you to speak for it until it's mature enough, and even then it could use as much help as it can to fulfill its potential.