Here again you've place science under a restriction it is neither obligated nor empirically qualified to adopt. Science in general is "the observation, identification, description, experimental investigation, and theoretical explanation of phenomena." If it cares to restrict itself to so-called "natural phenomenon" it is free to do so, but I would expect it to state outright that it has thereby arbitrarily eliminated explanations that may be objectively true.
No, this is you trying to lawyer things which are not science into the definition of science. Science deals with natural phenomenon. If something is "objectively true" but cannot be determined using the scientific method, by the empirical study of the natural world and natural phenomena, then the study and description of it is just not science.