Here's the thing about evidence and verifiability. Science is a framework which has proven extremely useful, for good reason. It distills out a sort of best practices for a kind of practical philosophy of approach that results in its practitioners being able to make more effective predictions about the universe around them. I would hope anyone interested in truth of any sort is keenly attentive to the benefits of exploring the world scientifically.
But the problem is that this is not enough. We are forced to live in all the dimensions of life, constantly, many of which are partly or entirely made up of decisions and beliefs (or at least tentative beliefs) for which we have no choice but to rely on unfalsifiable, unprovable hypotheses. I would venture to propose that most of our everyday decisions about how to live our lives, what to pursue, how to interact with other people, what is worth spending a life on, what is good and what is bad...basically our entire set of operating assumptions about the meaning of our lives is untestable, because we can't step outside of those lives, we can't see them from an objective point of view, we can't repeat conditions, we don't live consistently enough to isolate any of the possibilities as we'd have to do in order to measure things in a controlled test, and we won't be around in the end to see whether we were right (nor is there is any obvious way of measuring this even from the perspective of the "end of the story"). Plus, well, once we're dead, the outcome is not helpful, so we all live according to our best estimation of what life is about.
This doesn't by any means demonstrate that a particular faith of any sort has a basis in truth. The point is that there is no choice but to live by faith, because the knowledge we have about the whole deal, or even that we can possibly acquire in time to make any difference, is miniscule. The faith we're holding to might not be religious or deistic in any way, but no matter who we are, we're living according to some operating assumptions, and putting enough faith in them to make decisions based upon them, letting our lives slip away having applied them irrevocably to one or another path. And so, knowing that there is utterly no way to apply the framework of science to all of the matters concerning us, we have no choice but to use other methods of exploration as well, in order to build anywhere near complete enough a working model of how things are. Philosophy, theology, these are just that sort of exploration: ways of searching for understanding in the midst of this situation. One can't live without them, live "only by science", any more than one can make a successful and worthwhile journey by car taking into account only those truths that are clearly visible within the small bit of road directly illuminated by one's headlights.
(Even worse would be to insist that only the things that can be illuminated by headlights exist at all. Occam's Razor often gets shoved into the "science vs. religion" debates in a way that doesn't work. It's a very useful expression of the mentality one uses within science because it creates methodical practice out of what could be chaos. What it is not is any kind of proof of how things actually are. It is helpful to investigation to avoid multiplying entities unnecessarily. But is it true that there are no entities beyond those which are required to explain the currently visible portion of a phenomenon? We can't actually make that kind of positive assertion without resorting to exactly the kind of unfalsifiable truth claim that science supposedly doesn't care much for.)
But interesting you should mention critical peer review- in this area you'll not find theology wanting, at least not when it comes to trying. There is not a doctrine out there that isn't dissected, taken apart, put back together every which way, and run through the rigorous gauntlet of critical review, in many cases hundreds or thousands of years of such review. Of course, the whole thing lacking some of what you bring up (verifiability, etc.), this critical examination is hobbled somewhat in its ability to definitively rule out bad theories, but certain things still do apply; for instance, subjecting arguments to expectations concerning logic.
That definitely doesn't answer all of the pieces of your question, it is more a set of thoughts sparked by that question.
And you aren't playing under the same cost/benefit equation? Is it worth the fairly likely cost of the lives of several fellow insurgents or innocent bystanders to disable a tank for a matter of hours, only to see it back in action the next day? This is how occupiers can be successful- the price paid by insurgents is usually much, much higher.
Literally every time there's some new bit of Mac malware, we see a chorus of predictions in the form of "This is it, now the floodgates are going to open!" This has been going on for years, and these predictions have all been wrong. There are a couple of a new threats a year, and there isn't actually any particular reason to believe we're on the cusp of a dramatic non-linear increase.
* No bullshit. Make sure you get an itemized bill for your next surgical procedure, it'll piss you off what they charge for some of this shit.
I know someone who had to have a late-night imaging done once in the ER, I forget if it was an MRI or a CT scan. The bill had extra charges for overtime for the technician who had to be called in after-hours, and- I'm not making this up- also had extra charges for what amounted to after-hours overtime for the machine itself. I wasn't aware the machines had unionized or otherwise negotiated for extra pay when called into service outside normal business hours. It was only through looking closely at the itemized bill that they noticed this, and managed to argue the charge away, as there really was no justification the hospital could give for it.