I would add another definition for the word "complement." It would be:
v. to go well with
This is how people often use it. And I believe there's a subtle but clear difference between how people use it and how the dictionaries define it. Webster's New World and Merriam-Webster's give the definition: "to complete."
something that fills up, completes, or makes perfect -- Merriam-Webster Online
But it seems to me that's not exactly how people use it. When they say, "This wine complements the meal nicely," they're not always saying that it completes the meal. Often they just mean it goes well with the meal.
Plus, you often hear stuff like, "That wine complements the chateaubriand nicely" or "That rug really complements the couch." Clearly, these people don't mean that wine completes meat or that rugs complete drapes.
A dictionary's job is to report how the language is being used. And when it comes to "complement," I think they've been asleep at the switch. (Either that or wine drinkers know something I don't about meat.)