I think you missed the point of my post. The situations that you're referring to--a person claiming to read minds and so forth-- are situations that an ordinary person could put to the test without extraordinary effort. It's clear what the claim means and how to test it, and now super-advanced technology, security clearances, or anything like that are needed to test it. My post was about other situations, which an ordinary person could not test with a reasonable amount of effort. Consider the following three papers:
Deepak Singh, Amin Ahmend, Madhu Singh, Naval Singh. A Contraction Theorem Containing Rational Terms in Menger Spaces. Journal of Advanced Studies in Topology. Vol. 3, no. 3 (2012)
Madhuparna Karmakar. Electrostatic Potential in High-Temperature Superconducting Cuprates: Extended Ginzburg-Landau Theory. Advances in Condensed Matter Physics.Vol. 1 (2011)
Yan, D., Jin, C., Xiao, X.H., Dong, X.P. Antimicrobial properties of berberines alkaloids in Coptis Chinensis Franch by Microcalorimetry. Journal of biochemical and biophysical methods, Volume 70, Issue 6 (2008)
Personally I'm not able to understand a word in any of these three papers. I'm going to go out on a limb and assume that you can't either, since it's unlikely that you have adequate training in the necessary specializations. In any case, there are certainly some scientific and mathematical papers somewhere that you're completely unable to understand. So here's the question: do you accept the statements in these papers as being true?
If you answer no (and presumably treat literally millions of other scientific papers the same way) then I'd have to wonder how you can simultaneously defend science while not accepting millions of scientific papers.
If you answer yes, then there's no way you can know whether the contents are "logical, reasonable, and backed up by evidence." If you can't even understand the contents, you certainly can't rigorously determine whether they're logical, reasonable, or backed up by evidence. So if you answer yes, then you're accepting knowledge without holding it to the standards that you just gave.
Lastly, you could try to wiggle through the question without clearly answering "yes" or "no".
The question of what makes a doctor correct is a purely abstract and philosophical one. The question that we have to deal with is: if I'm desperately sick or injured, should I trust a doctor enough to let him treat me, or should I reject his treatment because I'm proud of not having blind faith in authorities? The Buddha once told a parable about a man who was struck by an arrow and in danger of bleeding to death. A doctor tried to treat him, but the man was only interested in asking an endless series of factual questins: what type of wood was the arrow made up? What bird provided the feathers that made the fletching? And so forth. Needless to say, the man died. The point is clear. An obsession with accepting knowledge if and only if it has clear, scientific answers when what's really needed is treatment and help will bring about disaster. We are all in a situation similar to the man struck by the arrow. Every one of us will be dead in, at most, a little over a hundred years. Moreover, each one of us may die today. To waste our time building little walls of scientific fact in our brains, walls that won't survive our death, would be a waste of time when we're in desperate need of salvation.