it's not a techincal criteria
The singular form of 'criteria' is 'criterion'.
You began by saying that a scientific education would have a negative effect. Your sole "evidence" doesn't even qualify as evidence, and it supports the position you are trying to oppose. The user you are speaking of clearly does not have a understanding of the scientific method. Let us re-examine the proposed situation from two perspectives, the scientist and the lay person.
A thorough scientific education would not fix everything, but it could help in many ways. Teaching people to challenge assumptions would rid us of many problems in the world today.
Even granting that science will often repeat experiments...
If the experiments are not repeated, it is not science. The scientific method requires repeated observations.
...at best, our "scientific" knowledge only proves the statistical likelihood of the result.
That is all science has ever done. We can never say that every electron in the universe carries a charge of -1.60218 E -19 C. However, every one of the multitude of electrons ever observed displays behavior consistent with that assumption. Therefore, it is likely (statistically speaking) that all electrons in the (local) universe carry this charge.
Long story short, provably determining what is real and what is merely imagined is far more difficult that applying the scientific method. However, applying the scientific method handily disposes of many impossibilities.