The experiments you are refering to doesn't violate relativity. Neither energy or information has been shown to travel faster than light (c), and this is the key issue when it comes to relativity.
The philosophical discussion is pherhaps better suited for another discussion forum. But let me just say that people proposing that "the objective reality", or truth, is created by belief and imagination will also have to explain why they don't throw themselves from the eighteenth floor, instead of taking the elevator. If they just imagine and believe that such an action won't hurt them, then it should also be true that it doesn't.