Unless, of course, these phenomena are subjective, in the literal sense of the word--if they are literally created by the observers, then the mere presence of a skeptic could prevent them from ever functioning, yet they would objectively function if all present were believers. And modern science would *never* confirm them, due to its basis in rigorous skepticism and objective verification. There have been some interesting hypotheses for quantum-based psychic abilities, and several of them would include strong observer dependence, thus making reproduction in controlled circumstances impossible, if those circumstances included skeptics.
And i'm not entirely certain this is off-topic. It would be a very interesting way to run powers (or magic) in some settings. It would be the logical extension of the imagination powers in Grimm, and goes right along with concepts like wild magic and the solipsistic spells (and some of the others from the Thought sphere) in 2nd ed. Not to mention, it's sort of a more extreme version of how illusions work in D&D, currently.
And it could be the basis for a far more interesting psionic combat system, one based on, basically, clash of willpower and belief between the various psychics--the defender attempting to convince herself that she really didn't believe in the attackers powers. Much like the way some people used to play illusions--if you gave any indication you weren't positive it was an illusion, you automatically failed your save (IOW, "no flinching").