Well, rather, it's not the strangers that are incomplete, but the strangeness of the unknown. To some extent there is a theory that we're all strangers to each other because our worlds and viewpoints have a limited ability to overlap. When it comes down to it, though, I think there are broad swaths of similarity.
These broad swaths are what artists (writers, musicians, poets, etc.) use to complete the picture they offer. I get different things out of a scene in a movie than the fellow chewing popcorn on my right, because my experiences are different. He's thinking, "This is a romantic love-story." I'm thinking, "This is a guy's rodomontade about his sexual prowess." It is this point that determines 'success' for many artists: whether or not the viewer appreciates the statement being made with their art. (There are some who deny any statement, although that is sometimes a statement in itself.)
The thought process here suggests to some extent that there is a level of success when the GM is no longer needed; when the PCs can walk around and interact with the world without him or her, you've reached the point where the message of the game environment has been translated efficaciously. At that point the GM's role has changed from a transmitter of the surroundings to choreographer of events, and finally, the director of motives, until, at the end, the GM is merely another actor in the role.
Of course, all the world's a stage, right?