Dear Constantin,
The FQXi is the "Foundational" Questions Institute. The idea is to probe the foundations of pre-existing theories, perhaps propose modifications to these foundations, or even (if absolutely necessary) to propose entirely new foundations. But really, proposing ENTIRELY NEW, completely original physics should be a last resort. I can think of no example where this method has been fruitful in the past. Take the discovery of special relativity, for example. There is a case in which the equations (the Lorentz transformations) were already "in the textbooks". Einstein reinterpreted them, employing a foundational analysis. Would you accuse Einstein of plagiarising here? An equation on its own doesn't tell us much. We need to know what it could mean. There are, in physics, usually (most probably always) multiple options in how we understand the mapping between equations and reality.
Your request for statements that "prove something about reality" must be, in the end, a request for a foundational (or interpretive) analysis (and an epistemological one at that). The point of many of these competitions (and the submissions) has been to probe just what can be said about reality GIVEN OUR THEORIES. You may think you are being a hard-nosed scientist, a la Feynman or Pauli perhaps, but you are in fact just espousing a very naive philosophical position. Feynman and Pauli might have spoken in a similar way, but their actual work revealed a very different, more sophisticated philosophical understanding.
Finally, I have to agree with Robert Spoljaric that your beef ought to be with FQXi.
Best,
Dean