I have run across a few people who claimed to be mediums.(In real life. I see them all the time on the internet) I have yet to meet any that were really mediums.
I do know someone who is what I call, psychic.
She knows things that no one else could possibly know. She meets total strangers and can tell you all about their childhood. She can tell you what someone is doing at any time. She can tell someone's future, what they will do with their lives. She has said, "He'll be dead before he's 30." and the guy died at 29, two days before his birthday. She knows the sex of a pregnant womans baby, before the woman even knows that she's pregnant. Stuff like that.
Yet, she works a full time menial job and has no desire whatsoever to proclaim her gift, unless it's life-threatening and even then she only warns the people involved and leaves their decisions to them.
When someone tells her that she is psychic, she adamently denies it and says it's only woman's intuition.
To me, she is a psychic, that has a true gift.
I believe that anyone who is truly gifted in this way, has no desire to be famous or rich because of it.
To her it is the norm and she doesn't like to call attention to it.
Now maybe she is just a really humble person, no actually she's not.

She just doesn't think that this ability makes her any more special than the next person. I admire her for that.
So yes, I believe that there are true psychics (and mediums) out there, but I believe that they are few and far between.
I agree that there should be some sort of testing for them. If you have the gift, then you have it. If you don't, then you don't. It really shouldn't make any difference what the test consists of.
This is strictly my opinion and isn't meant to offend anyone.