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I think the relevant wording here is "problem of induction". You can generate evidence at will and meetn any threshold of evidence for the statement "all swans are white". Anyone can perform the experiment by traveling around the northern hemisphere and find millions of white swans.

It would still be silly to call that statement a fact, because it only requires a single swan sighting in Australia to falsify it.

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You cannot "generate evidence at will to meet any threshold of evidence" for this specific example ("all swans are white") because, unless you posit that there are swans in Kepler-422B, I can set my threshold of evidence to "we have turned the earth into computronium and have not found any non-white swans", which is a finite (albeit large) threshold.

Once we agree on whatever definition of "swan" we care about (an animal belonging to a specific phylogenetic branch, with such and such qualities) we can agree on a more reasonable threshold, one that should include a visit to Australia to be crossed.

The problem of induction always applies. You also can't examine every bit of matter in the universe to ensure it is made of atoms.

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