These people, much like magicians, are masters at deception. Many of them are experts at making people think that they know more than they rationally should, or are doing more than should be normally possible, even though they really aren't. Even very intelligent and smart people may not be immune from being deceived.
For example, I find this quote from Wikipedia about the movie Red Lights very interesting:
Robert De Niro researched and met with psychics for his role and developed the cautious belief that there is something to the phenomenon based on allegedly psychically obtained information they were able to tell him that he insists only he knew: "There's no way they could have known certain things and they said them, so in that sense, I have no answer than to say that I have to believe that there's something there that they pick up psychically. I don't know what it is".While I of course don't know Mr. De Niro, I'm convinced that he is a very intelligent, smart and rational no-nonsense person who would never fall for simple scams that would fool most people. (And it's not like he's outright falling for it in this case. As his statement says, it's not like he is outright accepting that there's something supernatural happening, only that something yet unexplained seems to be behind this.) I'm sure that he is the kind of thinking and sharp person that would require very special tactics to deceive him into actually believing that there must be something genuine behind all this, rather than it being just pure deception.
But these professional psychics are masters at this. They are magicians: They know all the tricks in the trade in order to fool and convince the people who don't know these tricks. They are masters at making you think that they know something that they physically shouldn't be able to know.
Actual magicians know these tricks, and they are never fooled, because they know how the deception works. This is the reason why the best debunkers are magicians (rather than eg. scientists.)