Faith writes:
Does investigation actually "reveal some natural process at work," or is it just that if the investigator can dream up a plausible naturalistic explanation it's accepted without actual evidence?
In this case, it is a matter of the magicians knowing natural processes that can produce the same observations. In fact, they can demonstrate that those natural processes can produce those observations. Houdini was another famous magician who exposed the tricks that supposed psychics, mediums, and mentalists used. Randi, Penn, and Teller are continuing the tradition that Houdini started. What Randi does is set up an experiment where those sleights of hand, misdirections, and other tricks are taken out of the equation.
For example, Randi and most magicians can make a card appear out of thin air, or at least that's what it looks like to an untrained eye. There are several sleights of hand that allow you to do this. What Randi would do to see if this really were a supernatural event is have the magician strip down to limited clothing, examine the magician from head to foot, and then have the magician attempt to make the card appear. I can almost guarantee that no magician could make a card appear out of thin air if Randi set up the experiment.
I don't know why anybody would expect psychic phenomena to be produceable on demand, but since it isn't, that is made an excuse to dismiss the whole idea.
Uri Geller could make a spoon bend on demand, and he claimed it was due to psychic powers. Uri Geller was one of the first psychics that Randi exposed.