Brett:
In a typical magic effect, I think that the audience assumes that the magician did "something" to accomplish the effect other than what the magician actually did. For example, the magician "somehow" hid the signed card in the box rather than it dematerializing from the deck and rematerializing in the box. Hence, the term "illusion." We present the illusion of magic. In the same way, I think that spectators assume that, even though the assistant from the audience is "waiving the wand" that the magician did "something" to accomplish the effect. Nonetheless, the illusion of the assistant being the magician is there.
My philosophy is that we, as magicians, need to do two things. The first is to eliminate any rational explanation for the method to the effect subtly (typically through the construction of the effect). By subtly, I mean not beating the spectators over the head by saying "this is an ordinary deck, all the cards are different, it is really shuffled and you had the choice to pick any card." Rather, let the spectator shuffle the deck, use a method of selection that seems fair, show the spectator the rest of the deck after they have picked their card (thus proving they are different and shuffled). The other strength of many of these effects is that they appear to be done entirely by the spectator (not having the spectator just say the magic word). The second is to present the illusion. This is all scripting and acting. The goal is to answer the question of "why" the magic happened (notice, I didn't say "how"). Chad Long's shuffling lesson, as I learned it from Wayne Houchin's presentation on Art of Astonishment, has a good "why" in that Wayne explains "he who cuts the deck, controls the game." The spectator cuts the deck and therefore, they control the game. Tamaritz's Paradise Recovered in Verbal Magic has the spectators draw a picture representing their idea of happiness on cards and then visualize letting go the things that hold us back and tossing the cards representing those things. In the end, they are left with one card - the card on which they drew their vision of happiness. Jim Steinmeyer's The Magician Who Fools Himself has the spectator playing the role of a magician, doing a trick that the performer had seen before. In each of those effects, the presentation presents a powerful explanation of why the effect works.
If we eliminate rational explanations and provide a powerful narrative of why the effect works, the spectator will buy into the illusion of magic. In many ways, they did perform a magic trick, but they realize that the magician had something to do with it -- even though they can't figure out the something. However, the illusion is so powerful, they want to believe it.