The world of ideas is cluttered with nonsensical references to supernatural and paranormal events. While some of these hypothetical events cannot be disproved, it makes no sense to refer to them as supernatural. If they are more than just imaginary, then they are detectable through measurement. If they are impossible to measure, then they are not events or phenomena and are merely imaginary.
For example, an alien spacecraft either crashed near Roswell, New Mexico in 1947 or did not. If one did, it would have been possible to observe the spacecraft physically—by viewing light reflected off of it, or perhaps by analyzing its wreckage and impact crater on the ground. Evidence of a particular phenomenon may be difficult to detect and interpret, but it nonetheless must exist. If we detect no evidence of a spacecraft near Roswell, it would mean one of two possibilities—that no spacecraft landed in 1947, or that one did land but the evidence is too subtle for us to understand. What makes no sense is to say that a spacecraft did crash, but that no evidence exists in the physical universe.
When a scientific theory fails to explain strange phenomena, then it is not a good theory. But the natural world is far weirder than anything ever imagined by theologians, psychics, witch doctors, or UFO hoaxers. Physicists have observed phenomena on the quantum scale that eludes all human intuition, and the same is true about very large scales. Just because something is weird does not mean it is supernatural.