I'm skeptical about almost all people who have convinced themselves that they are gifted, even when it is demonstrated to them that their "powers" only work occasionally.
Personally, I find NDEs more fascinating, and still put some stock in Howard Storm's NDE (he never wrote a book, but it changed his life, as NDEs change many people's lives, and I've heard him tell his story on cassette tapes a number of times (no charge, he's not making a cent off it, not even now, he converted from being a class A jerk to quitting his cushy job as chair of the Art Dept. at a university and became a liberal Christian minister). And I put some stock in a few other NDEs. I also admit that part of the reason I do this is because some NDEs make sense to me, like Storms, and the kind of heaven they describe makes sense to me, a skeptic. And I WANT to believe it. By the way, one of the greatest, or at least one of the most prolific skeptical minds of our time, Martin Gardner (who writes a regular column for CSICOP) also happens to believe in an afterlife, though he admits he hasn't found any proof for it yet, still he argues that there is no necessary reason to deny it in his book, THE WHYS OF A PHILOSOPHICAL SCRIVENER.
I also agree that mediumship and "cold readings" strike me as having a lot in common with Pat Robertson's nightly stabs in the dark at the illnesses of his viewing audience, some of whom inevitably call him to say that they are sure he was speaking about THEM, and now they are cured (even when the show is a rerun of a tape Pat made earlier). I think Pat is sincere and he thinks his random naming of illnesses is being given him by God, and many mediums think their random calling out of things that "hit upon" are due to "supernatural" powers or beings making them "hit the nail on the head." But then, maybe a lot of it is just guesswork inserted in and around occasional true visions that happen a lot more rarely than psychics think they happen. I mean once you have one true premonition you start seeing them everywhere, you start to mistake every little coincidence in your life for a miracle and you start to mistake yourself for a great psychic. The same things happen to people say, in public office. Once they get elected they start to mistake themselves for politicians, and start to speak like politicians, walk like politicians, etc. We all wear many masks in life. And we all may have certain things we are very good at, or even may have occasional inexplicable bits of insight of maybe even an occasional supernatural encounter, but that doesn't mean we're good at everything or always being led by spirits, nor does it mean that demons are everywhere, though they might be in a few places (as even the Catholic church admits, true possession is very very rare). I think as human beings we make everything out to be larger than life, even our skepticism. Deep down, the skeptics and the mediums both wanted to be right, they wanted a clear cut across the board vindication of their positions, their ideas, but nothing in nature or the world is that clear cut and both should be humbled. Maybe Edwards occasionally does have or has had a supernatural insight about someone. Maybe most of the time, it is just wishful thinking and coincidence and nobody is truly a "medium." So, maybe there's some truth to both sides, with of course, the majority of the time being fodder for skeptics.