(nods) This is basically (modulo snark) the position of several people I know who believe in such things, and at least one LW contributor.

Faced with that response, I usually pursue a track along the lines of "Ah, I see. That makes sense as far as it goes, but it gets tricky, because it's also true that we frequently perceive patterns that aren't justified by the data at all, but without systematic study it's hard to tell. For example, (examples)."

Followed by a longish discussion to get clear on the idea that some perceived patterns are indeed hallucinatory in this sense, even though your cousin's psychic power isn't necessarily one of those patterns. This sometimes fails... nobody I know actually claims that all perceived patterns are non-hallucinatory, but some people I know reject the path from "not all perceived patterns are non-hallucinatory" to "some perceived patterns are hallucinatory." Which I generally interpret as refusing to have the conversation at all because they don't like where it's headed. a preference I usually respect out of politeness.

If it succeeds, I move on to "OK. So when I see a pattern that goes away when I begin systematic study, there are two possible theories: either the phenomenon is evasive as you describe, or my brain is perceiving patterns that aren't there in the first place. How might I go about telling the difference, so I could be sure which was which? For example, if I wake up in the middle of the night frightened that there's an intruder in my house, what could I do to figure out whether there is one or not?"

Which moves pretty quickly to the realization that an intruder in my house that systematically evades detection becomes increasingly implausible the more failed tests I perform, and at some point the theory that there simply isn't such an intruder becomes more plausible.

I generally consider this a good place to stop with most people. Lather, rinse, repeat. They have one track that supports "I believe X no matter how many experiments fail to provide evidence for it," and another track that supports "the more experiments fail to provide evidence for X, the less I should believe X". They tend to mutually inhibit one another. The more that second track is activated, the less powerful that first track is; eventually it crumbles.