But science rules things out by falsifying them, not because of a lack of evidence for them... those things it just ignores.
No, not really. A scientist might perfectly well write: "Of all extant animals, only birds, bats, and insects can fly." This is not because pigs with wings have been
falsified (one can only falsify a universal and not a particular proposition) but because there is no evidence for them --- that is, because the proposition that pigs
don't have wings has
not been falsified.