Here is an easily understand analogy of what you are saying, I will refer to it as the AoE rule:
Monk #1: "Your God doesn't exist because there is no evidence that it/he/she exists".
Monk #2: "My God definitely does exist because you cannot prove that it/he/she doesn't exist".
Unfortunately there is no standard in how this rule is applied and it tends to be used at people's discretion - they are happy to believe and live their lives based on a belief despite absence of evidence, yet they are quick to use the very same rule to dismiss things they personally don't want to believe in.
By definition, the absence of evidence in itself doesn't prove that something doesn't exist, it simply lowers the probability that it does exist.
Let me be clear that this is an issue that the community has to deal with and find a happy medium - it is not something that the moderators or SE staff should ever have to become actively involved in.
The primary aim of the Stack Exchange group of sites is to provide a high quality repository of information about each site's subject matter. Depending on the site the material won't always be conclusively provable, if it isn't then it should still be at a academically or empirically defendable level.
The AoE rule should be used as a request to get more information. If someone uses the AoE rule to debate a point made by the OP, then the onus is on the OP to provide further proof or references (in fact we have a post notice for that very thing that moderators can afix to posts). However that doesn't grant the right for people to use the AoE rule as a wrecking ball to dismantle any particular statements they don't agree with. If a request is made for more information and that information isn't forthcoming then the community already has all the mechanisms it needs to address the credibility of a post - it can be down voted and then deleted.
Community members should also cut each other some slack when it comes to descriptions of techniques, effectiveness or phenomena - it can be difficult to describe something physical with words in a textbox. If something doesn't make sense then seek clarification before you dismiss it. If someone seeks clarification from you then don't be upset by that - they're not in your head space and complex things can easily be misrepresented or inadequately described.
Further to this, remember that there is a chat room available for ongoing discussion. Comments should be used to seek or give clarification or context, they shouldn't be used for conversation or as a battle ground.