I think the problem is the floating definition of the word "concept." In ad school, they teach you one definition, which revolves around the idea that the consumer must bring a bit of himself to the work in order to understand it. But I've heard people use the word concept as a synonym for "theme." And as a synonym for "cool to look at..." [T]he word concept is like the word edgy - so overused it borders on meaningless.
I can't remember who first explained the word concept to me. It was probably one of my teachers at The Creative Circus. But I've always found the following explanation interesting.
Consider the three arcs to the right. In each, the "A" represents the product and the "B" represents the ad.
In the top arc, the product and the ad are right up next to each other. There's no room for the consumer to have fun with the ad, to feel a connection to it. The headline is probably something like, "Today, you can buy this chair for $99." And the visual is probably a chair. This is not a concept.
In the middle arc, the product and the ad are nowhere near each other. Nobody could make sense of this ad. The headline probably says, "Attila the Hun loves you." And the visual is probably a boat, upon which sits a hippo. This is not a concept.
But the final arc is. The product and the ad aren't smothering each other, but they're close enough to make the consumer feel the shock of recognition and a bond with the brand that transcends any short-term product offering.
Of course even that labored and lengthy definition can't possibly explain something as good as this: