The idea of the burden of proof belonging to whoever makes a claim is very prevalent but this is an overly simple view of how we should assess claims.
When presented with a claim the origin of that claim matters. Random speculative assertions don’t get the same prior probability of truth as claims based on established evidence or even those of speculative but well grounded claims about reality. Understanding this fact is why the statement “black holes exist” isn’t treated the same today as it would have been 80 years ago. This principle, broadly speaking, is also why we care what the origin of a claim is and what lends credence to experts over the average person.
All ideas and claims are not generated equally. This sounds simple enough right? Surely no one would make the claim we should give the same probability of truth to a claim made by a repeated liar and someone who rarely, if ever, lies or is wrong?
We all apply this idea, otherwise we would forever be rechecking the validity of every statement made by everyone, yet apply this to new age or miracle claims at your own peril. I can’t recount how many times I’ve heard some individual claim some individual “natural” or “organic” product is the cure for cancer. Not surprisingly, considering cancer is still around, none of them have turned out to be true. Similarly when assessing any new miracle claim from a holy book I don’t give the new claim a 50/50 chance of being legitimate because every holy book I’m aware of has yet to produce a single example of such a feat despite thousands of years worth of claims to the contrary.
If “organic” cures to complex diseases, the Bible or the Qur’an had a flawless, or even good, track record of truth I would rate the prior probability very high and strongly consider checking to verify such claims. As it stands these claims have consistently and unanimously turned out to be false so it’s overwhelmingly more likely to turn out to be a waste of time to even check. This isn’t to say the evidence supporting a claim isn’t the most important factor in accepting claims but merely that you are right to give a low prior probability of truth to assertions of questionable origins.