That raises a possible / probable principle for discerning between rare observations on the one hand and unjustified ones on the other, and a chief limitation of empiricism.
Empiricism rests on the assumption that the Universe and phenomena in it are fundamentally observable. Which means that phenomena generate some kind of interaction with their surroundings.
Observability is depenent on the frequency, strength, certainty (as opposed to ambiguity), of those interactions. There's a strong association between the sensibility of phenomenon (our ability to see, hear, smell, feel, or taste it directly) and its believability, though also with recordability. "Capturing something", on film, tape, audio, or other sensing devices, is key to demonstrable proof. (In its absence we're mostly limited to testimony or second-hand accounts. Durer's Rhinocerous is a wonderful example of a second-hand account, visualised in detail. It's almost dreamlike, startlingly accurate in some particulars, oddly off in others.)
Empiricism does most poorly with rare or hard-to-sense phenomena. Literal black swans, neutrinos, the interior of the Earth, subatomic particles, the boundaries of the Universe, interiors of stars, black holes and neutron stars (massive, but not very emissive). Or the very long ago (think evolution and geology). Epidemiology and statistical methods for rare and distributed events. Various sensing, visualisation, microscopy, telescopy, tomographic, and other methods.
Even in cases of very difficult-to-sense phenomena, though empiricism tends to improve in its resolving capability with time and improvement of methods. And where those capabilities improve, rare-but-real phenomena are more revealed over time. The distant (or small, or remote in time, or hard to percieve) becomes clearer. Presumed-extinct species are found. Hidden structures within the Earth are visualised, and correlated with other events (see the evolution of the concept of plate tectonics, one of my favourite instances).
Where the phenomenon is not real, though ... it either decreases in prevalence (mostly in the case of frauds), or in the case of "edge-of-perception" sensing, in which random noise is mistaken (or hallucinated) as actual, remains roughly constant over time.
Spellling all this out, I'm all but certain there's an established concept built around this (or several). Though it seems a useful heuristic in determinng likely validity or falsity of phenomena given enhanced sensing or recording capabilities.
UFOs have remained frustratingly ellusive. Meteorites have become stunningly compelling. Footage of accidents, abuses of power, or casual racism are now starkly evident (if often undeterred by the fact of video). And so on.