I think some can but there are lots more who can't!
I did have one session with a medium many years ago and I was very impressed. This lady worked from her own home and is not on the stage and doesn't take money etc. I already knew not to give her any clue as to my identify, marital status, career or family background etc. and I actually tried to throw her off the track, but she wasn't put off, was very accurate and yes, a number of things she told me about did happen. So with this lady, yes I was very impressed.
However, I think this caliber of medium is not that common and many are rubbish. The thing is, the false ones are so good at picking up on physical and psychological clues as well as subtly getting information out of people, that at first folks are quite impressed. But they are not doing anything other than being good at guessing, excellent at back-tracking and covering up their mistakes.
The difficulty with the genuine ones is that investigators use physical means to test what is a non-physical thing, so at present it's not possible to definately say that what genuine psychics/mediums do is legit. I personally think that a few do have an ability that is extraordinary.
The best medium I ever saw (different to the one mentioned previously) was David Wells from Scotland and yes, I do believe this man is genuine. But it doesn't surprise me at all that many people find it all a bit dubious when you see what nonsense is shown on TV etc.