That's fine, but the claim is "you can't prove a negative," not "you can't refute a negative" - I don't think your example refutes that claim, speaking of refutation.
Anyway, the claim itself tends to be reflective of the difficulties inherent in demonstrating the truth of universal negative propositions. If I say that there are no green unicorns, the only way to demonstrate whether that's true or not would be to undertake a detailed examination of the entire universe, looking at every portion of it simultaneously, lest the little green unicorns hide someplace I've already looked - in essence, to demonstrate to you that this proposition is true requires us both to be more or less omniscient.
Of course, some negative propositions are rather more specific - "there is no butter in my refrigerator" is somewhat easier to verify. Needless to say, all this doesn't exactly make a nice soundbite, so "you can't prove a negative" is what's remembered, despite being a bit simplistic ;)
You speak as if the refutation of an explicit statement had no bearing on the truth or falsity of that statement. To prove a statement false means that we no longer have to behave as if it's true -- a rather important result.
The real problem is that "You can't prove a negative" is self-defeating: the statement is itself a member of the supposedly unprovable set of "negatives." At best, therefore, it's logically meaningless.
However, one can in fact produce cases whereby one proves a negative -- this is often done in mathematics, for example. The point being, of course, that you can prove a negative, at least sometimes; and thus the original, general, statement is seen to be not just meaningless, but actually false.
The upshot being that, unfortunately for some, they must actually exercise rational thought, rather than hide behind the now-refuted statement that "you can't prove a negative."
If I say that there are no green unicorns, the only way to demonstrate whether that's true or not would be to undertake a detailed examination of the entire universe, looking at every portion of it simultaneously, lest the little green unicorns hide someplace I've already looked - in essence, to demonstrate to you that this proposition is true requires us both to be more or less omniscient.
Or, I could simply hire a genetic engineer to create one.... ;-) (BTW, back to my example, there really are a few green mammals.)
Still, your example is interesting from a couple of perspectives. First, it gets most of its force from our a priori presumption that green unicorns really don't exist -- it verges on the fallacy of affirming the consequent. We'd be far less impressed by your "universal, omniscient search" if we knew exactly where to produce the green unicorn that would refute your claim to the contrary. You wouldn't get much mileage out of it if you based your example on "there are no black cows." Second, the example puts you in a position of having to define explicitly and exactly the characteristics of a "green unicorn" in such a way that your statement cannot be refuted by my simply producing any one-horned animal that happens to be green -- an oddly colored narwhal, for instance.
Be that as it may, the interesting thing about this particular topic on this particular thread is that the people committing the supposed fallacy are those who say "Intelligent Design Never Occurred."