This argument is based on an assumption that science deals in eternal absolutes. That luxury is generally the preserve of, well, philosophy.
Science deals with hypotheses and experiments. I can test the hypothesis that there exists black swans. And, by luck, I can confirm it readily (as I did last weekend).
Now, if I try to confirm the hypothesis that there exist green swans, I cannot do so so readily. However, assuming my grant money comes through, I can set out on a series of expeditions to look for this elusive creature. As my fruitless search expands, I may not be able to prove categorically that no green swan exists anywhere (my grant money doesn't stretch to searching Jupiter). I can, though, make strong statements about their existence within the bounds of my experimental scope.
And it's this latter point that is key. It's why, for example, people say that Einstein proved Newton wrong. He didn't. He showed the bounds within which Newtonian mechanics apply and the adjustments one need to make to extend the bounds.
And it's why, even when my best seller There are no green swans is reaching its 30th edition, one is discovered in the depths of the Amazon jungle, I will rejoice. Apart from making a great sequel, our knowledge has progressed. Our original understanding was limited and we can now correct our hypothesis.
Some people find this lack of absolutes unsatisfying. Personally, I think it's a swanderful.