According to my Dhamma teachers, a person can make tons of progress in the jhanas, and acquire some of the reported extraordinary abilities, without necessarily attaining as much in the way of wisdom or morals. I have been cautioned about this by my teachers on more than one occasion, and my understanding of it is that it has to do with mindfulness and responsibility.
Some years ago I had the great privilege of reading a really disturbing little novella called "Childhood's End" by Arthur C. Clarke. In the story, the world is suddenly visited by an alien race whose intelligence and strength far surpasses our own. They assume a benevolent (but secretive) control over the affairs of humanity, and each decree they issue produces peaceful and wise results. But one of their decrees is met with bewilderment, and that is that the space programs of all nations are to be immediately ended. The only explanation they give is this: "the stars are not for Man." It turns out that humanity, in its current state, would have done little except play out our defilements upon a galactic scale, and the results would have been catastrophic.
I think this is how I view these abilities. As in our current world, we have some truly amazing resources - the Internet, uranium enrichment, genetics, renewable energy - which are truly amazing in their potential, and yet can be cataclysmic in the hands of people (no matter how scholarly they may be) whose lives are controlled by lust, anger, and delusion.
So, now comes the question of whether or not I actually think such things are real or not. The truth is, I just don't know. I come from an empirical background too, so I admit I am biased against such claims. I have not yet seen anyone predict the future in some falsifiable way. I have never heard anyone even claim to speak with the departed dead, but I'm not sure that ability would be of much use anyway. I have, however, had people who were experienced meditators give me guidance that was so stunningly specific, so insightful, that I couldn't help but wonder if they had some special insight into my mind.
But I guess that's it, isn't it? Maybe these "gifts" are a lot less miraculous than we give them credit for, and really they amount to the subtle workings of a very calm and disciplined mind. Not so much "supernatural" but more "uncommon." I'm not even sure that "supernatural" is a meaningful word anyway.


