That gets down to some very basic issues in epistemology. I did my doctoral work at a highly secular university philosophy program, but the epistemologists and probability theorist that I worked with, who certainly were not religious people, thought that classical foundationalism was a very problematic doctrine, and that the idea that a limited range of beliefs belonged in the "core" while other beliefs had to be proved by evidence, is in fact an unsupportable position. http://www.unc.edu/~theis/phil...
As a result, they were in general skeptical of the claim that one particular position as opposed to another had "THE burden of proof." To say that the burden of proof lies on one side or another that we know always, what beliefs can be accepted without proof and which ones need to be demonstrated, and that project doesn't look to be achievable. Descartes, for example, said that he would doubt everything and believe only what could be proved, and most people think his project didn't work. He started by doubting sense experience and then had to appeal the theological arguments to defend his belief in an external world. Hume's empiricism left him in a position where he had to "justify" the idea that the future will resemble the past simply by appealing to custom and habit. In other words, we really don't have justification for it. In other words, Hume avoids having to justify the belief that the future will resemble the past by claiming that belief this belief doesn't have the burden of proof.
From this one could conclude that you can show that just about any belief is unjustified simply by putting a heavy enough burden of proof on it. If you could only justifiably believe in the external world if you could prove that you aren't a brain in a vat, that might prove difficult.
So, for example, as I learned Bayesian theory, a popular theory was that prior probabilities were subjective, and that people who had different one could in theory eventually come to a consensus by adjusting their probabilities as evidence came in, but the idea of a "proper starting point" or "correct priors" was considered misguided. One of my teachers (again a religious nonbeliever) said that "you are justified in believing what you already believe, unless you have good reason to change your beliefs." I remember asking him about Descartes method of doubt, and in response he mentioned an ancient Greek skeptic who sat on the marketplace wagging his index finger because he couldn't believe anything. In other words, what I learned from the study of epistemology led me to the conclusion that fixing the burden of proof is pretty difficult, and that it is hard to discover a "proper" position for the burden of proof. There are relative burdens of proof that different individuals have for certain claims, but a "correct" location for the burden of proof seems to me difficult to justify.
So, for example, when I first encountered the Outsider Test for Faith, it looked to me as if it was another case of implying classical foundationalism, or perhaps, applying classical foundationalism to religious belief in a way that it is not applied to other types of beliefs, and some of my early responses to the OTF came from this perspective.
If you think the key to refuting religious belief is to inculcate a proper epistemology, which results in a proper location of the burden of proof, then I am likely to be pretty skeptical of that enterprise, and my skepticism comes not from my religion, but rather from widely held views in epistemology that I got from secular philosophy teachers. I'm not saying that these epistemologists couldn't be wrong, but it might take a little work to convince me that they are wrong.