I'm wholly unconvinced that the ability/inability to read images on cards ( or indeed any other scientific test ) is proof of the absence or existence of psychic or mediumship skills. But being a believer myself (and believe me I believe in very little) you would expect me to say that wouldn't you?
The ability to read the cards (by which I mean, to correctly predict, without trickery, what is shown on a card that is not visible to the psychic) would be evidence of an ability so far not known to science. If it were to be done with suitable safeguards to prevent charlatanism, and the psychic was consistently right, significantly more often than random guesses, then it would have proved something. Whether you choose to call that "psychic" or use some other label, it would be of that ilk.
Inability to read cards is evidence of nothing except that you cannot read cards.
Absence of evidence is not evidence of absence. The fact that no one has yet demonstrated the ability under experimental conditions does not mean that the ability does not, or cannot, exist.
However, absence of evidence that would normally be expected to be available is evidence (but not proof) that the phenomenon does not exist. After all these years, decades, maybe centuries of people searching fr the evidence and offering prizes to anyone who can demonstrate the ability, the fact that no one has done so is at least strongly suggestive that the ability does not exist.
Comparison: reasonable evidence:
I spent 11 years in an insurance fraud investigation team.
Evidence merely points towards (or away from) something, but
proof definitely establishes that it is (or is not) the case.
If a customer said that they had a 6 year old hammer drill stolen from their garage, the fact that they did not have a receipt or manual would not automatically invalidate their claim. The absence of evidence would not prove that they did not have the drill. It is not an unreasonable claim and the absence of evidence is not unusual in the circumstances, and the claim would normally be paid.
Now imagine a customer who says that he had a month old Rolex watch worth £5,000 stolen. He cannot provide a receipt, manual, guarantee, certificate of authenticity, or bank or credit card statement showing the purchase. He has no photos of himself wearing the watch. He cannot identify the jeweller who sold it, or describe the watch in detail. he has no crime reference number. There was no damage to their door or window locks, and no sign of the alarm being activated.
The theft of a fairly new £5,000 prestige watch is extraordinary, and some, probably most, of the evidence listed would normally be available.
The insurance company would be entitled to refer to the absence of evidence that would normally be expected to be available, and reject the claim. However, they would not have
proved that the claim was fraudulent; the customer would have failed to
prove that it was valid.
Carl Sagan was not quite right when he said "extraordinary claims require extraordinary proof" but it is certainly the case that extraordinary claims require more evidence to back them up than routine and unsurprising claims.