Speaking as a scientifically-minded person, the point really is, as usual, that the onus isn't on "science" to provide answers, but the proponents. That aside, what scientists can do, at least, is to provide something of a "checklist", that any particular claim of a genuine "paranormal" incident ought to be tested against before the claim should be taken more seriously.
I can't say I can provide an exhaustive list of what should be on the checklist, but essentially it would range from eliminating all of the more mundane (or sinister) explanations for what happened. It's not difficult to find cases of self-proclaimed psychics who turned out to be deliberately fraudulent, for example. Doesn't have to be deliberate, either. In one fairly famous, related example, a German horse owner claimed that his horse was able to count and perform simple arithmetic. It was, in fact, demonstrated that several things were true:
(1) The horse owner (von Osten) wasn't at all being dishonest, and genuinely believed that he'd trained his horse to count;
(2) The horse couldn't count as well as von Osten thought it could; and could only get the answers right when von Osten knew them himself -- and when the horse could see von Osten.
(3) Or, indeed, this was true with any other person.
(4) Turns out that the horse (Clever Hans) was relying on certain subconscious cues that it should stop "counting" given away by the questioner, eg tensing up when it was nearly time to stop and relaxing when the "last" tap of its hoof was made.
Now, for the record, I am by no means claiming that the psychic your friend saw was relying on essentially the same tricks or cues or whatever as the horse was. What I *am* saying is that the sort of testing the horse went through, is required in order to rule out such explanations and leave only the truly "paranormal" -- whatever that may turn out to be.
Science has a tendency to stick stubbornly to what it knows, or thinks it knows, until it has no option but to let go in the face of overwhelming evidence. Whether that's a weakness or a strength is a matter of opinion, perhaps. For myself, I think there's something to be said for being careful not to get too excited every time you think you've hit on something new that shows previous scientific orthodoxy to be wrong, and to test very, very carefully indeed whether your new ideas are right after all.