If someone consistently scored 15 right guesses of 25 Zener cards then yes something is going on. However this doesn't "prove" physic phenomena at all all it "proves" is that something is likely modifying chance. What could that be?
Well if it happens only once I would say chance is most likely. Not some paranormal power which cannot be measured or shown to exist. If it happens again and again then what is more likely some psychic power, we can't detect at all, or something else? Well I would argue that the more likely explanations are outright cheating or unconscious sensory cueing. It only takes a small bit of either one for someone to have results that are millions or billions to one.
Zener cards are particularly notorious in this regard. the ways to cue, cheat etc., when tested this way are legion. Rhine the Parapsychologist who devised them in the 1920s was notorious for his lax standards. He believed that negative results should not be published. Stopped "runs", (A series of tests with the cards.), when the results began to drift towards chance. His subjects tended to lose their powers over time, with more and more tests.
When Rhine found out that more strict experimental protocols led to chance results he concluded that strict conditions "upset" his subjects and thus inhibited psychic powers. And Rhine frequently let his subjects run the experiments. Today his research with these cards is not highly thought of.
Has for ways of cheating. Well sometimes Rhine's Zener cards were so poorly made you could see the symbol, with the right light through the card. The cards could be nicked or otherwise marked according to the symbol on it. If the giver of the test was wearing glasses, sometimes you could see the cards in reflection in the glasses. And sometimes this was possible just looking into someone's eyes! Remember none of these methods has to be perfect; all that is necessary is enough information to bump up your score just above chance and after say 1000 runs you have results that are billions to one!
And of course there are many other ways to do it. And if you are willing to cheat the skies the limit.