I think that one cause of this "puzzle" perception of magic is the fact that we, magicians in general, concentrate too much on the tricks, as if they are the essence of the performance. I believe the tricks should be merely manifestations of the magician's character, so that, rather than someone being fascinated by your abilities with a deck of cards, they are intrigued by you as a person. Uri Geller, Derren Brown, David Blaine and Criss Angel have all acheived this, in that they, in the public's mind, are more than the sum of their tricks. People are interested in them as people.
Once you've established a strong character, some of your effects can be presented as a puzzle, or explicitly as sleight-of-hand, while still maintaining their magical impact. The key to it is to decide who you are as a magician. Are you genuinely psychic? Are you a master of underground card cheating techniques? Are you a comedian? Then, your choice of effect and style of presentation should all be informed by this persona. This does mean that you limit your choice of suitable tricks, but it means that your performances will be infinitely more interesting than a series of disconnected routines.
So, my view on this, is really that we worry too much about whether our tricks look like puzzles, or whether the audience can tell it's sleight-of-hand. Real magic comes from the intimate theatre, the connection between you and your spectators, regardless of what trick you perform or what "Presentation" you use.