However, it's equally false to simply assert that all AOWK are automatically false, because there are in fact many ways of "Knowing" besides the scientific method. A variant of the "AOWK fallacy" fallacy is presented by another blogger "Skeptico" here, as follows:
Here is another fallacious argument skeptics will have heard:
>> There are ways of knowing other than the scientific one
>> The scientific method is not the only source of truth
..or similar wording. It is an appeal to other ways of knowing apart from science. The claim is that the tools of critical thinking and science are not sufficient to evaluate the believer’s claim; therefore the believer's claim has validity despite the lack of evidence for it.
The flaw in the argument
No one is claiming that science has all the answers or is always right. However, science has proved to be the most reliable method we know for evaluating claims and figuring out how the universe works. If the believer is claiming that there is a better method, it is up to him or her to justify that claim. To demonstrate this, believers need to explain their better method for evaluating claims, and provide evidence that it is indeed a better method. If they cannot do this their appeal to other ways of knowing is vacuous and fallacious.
Emphasis above differs from the original. Let's start with their definition of AOWK. I think it's pretty obvious that there are ways of knowing other than the scientific one. And that it's fairly obvious that the scientific method is not the only source of truth. Example: My knowledge that my love for my wife and child exists today is acquired without the scientific method, and the scientific method cannot explain why that love endures. Another example is in chaotic systems, which are ostensibly deterministic but elude rigorous predictive description. We can forecast the weather and the stock market, but we cannot truly predict it. The various industries that have sprung up about these disciplines rely on interpolation from past observations, not a total characterization of future behavior. In a nutshell, stochastic phenomena are beyond the Zen of science, and lie more in the realm of probability and uncertainty - and this fuzziness is hard-wired into the fundamental substrate of the Universe itself, much to the consternation of great minds like Einstein himself.
Likewise, it is simply true that sometimes, the tools of critical thinking and science are indeed insufficient to evaluate a given claim. This too has basis in fundamental reality; Gödel's Theorem has profound implications on the boundaries of reason. In a nutshell, Gödel's Theorem states that for any rational construct of axioms and theorems, there are always statements that can be neither proved nor disproved. Or as Jones and Wilson put it,
You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules and axioms, but by doing so you'll only create a larger system with its own unprovable statements. The implication is that all logical system of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.
The main thrust of Skeptico's argument however is that he requires someone who believes something to be true to provide evidence that the mechanism by which they believe is superior to science. It is not clear to me how a given system for evaluating a statement can be said to be "better" or "worse" then another in a quantitative and meaningful way. What is the metric? Skeptico seems to implicitly assume that an answer arrived at via science is inherently rigorous, but that's not the case. Example: Neither Newtonian mechanics nor Relativity suffice to describe the N-body problem. However, they do represent stages of an asymptotically improving model of the Universe. But for such a model to accurately encompass the totality of complexity within the Universe, you'd need a model as complex as the Universe itself. Hence, you can never be sure that the truth you are describing via Science is as immutable as Truth. This anti-dogmatic trait of the scientific method is a strength, not a weakness.
Therefore, the demand that an AOWK be supported with "evidence" of superiority to science is a standard that science itself can not meet. A hypothetical example might be a meeting some centuries ago between someone who empirically shows that the planets revolve around the earth, and a scientist who has a mathematical model for a heliocentric universe. Based on the evidence that both bring to the table, neither can say with certainty who is correct. That we accept heliocentrism today is because we do have Relativity to explain the discrepancies of Newtonian mechanics, satellite observations, etc. But simple skepticism is not enough by itself to disprove the AOWK - the best you can say is that there is room for disagreement. The only time a scientific argument can "win" is if the latter has direct evidence disproving the claims of the other. Absence of evidence is not evidence of absence - and to claim otherwise is to make a fallacy of one's own: the Argument from Ignorance.
 Also see these previous posts: Waiting for Gödel, the falsity of the Kalam Cosmological Argument, and Flew's Wager; also see the evolving conversation at Super-rational blog.
 Highly relevant here is Thomas Kuhn's philosophy of "paradigm shifts" within scientific orthodoxy as occurring as "revolutions" rather than an incremental accumulation of knowledge. One case study is the theory of plate tectonics: Alfred Wegener first observed evidence for what he called "continental drift" as far back as 1915 but faced extreme resistance by the scientific community, who held to a more static view of the earth with change primarily driven by heating and cooling cycles. Today there is virtually no one who does not accept plate tectonics as the unifying model of geologic change.