If you 'know' it - you should be able to articulate the source of the belief.
That is an interesting proposition, which I would actually call a bias rather than a principle. Why should be able to articulate the source of your knowing for it to actually be knowing? Note that I'm not asking whether it's
useful to be able to do so; of course it is. But we are talking about whether you
can know something that you cannot articulate. So that depends on what knowing means. If we simply set as an axiom that knowing is when you can articulate it and show where it came from, then tautologically that will obviously be what you have to demonstrate in order to say you know something. But that's only because you've axiomatically said so. That's why above I mentioned that your definition is self-referential.
But let me suggest a few scenarios and you tell me whether this counts as 'knowing' something:
1) You meet a stranger, get a weird vibe from them, and feel nervous and keep your guard up.
-Is this something you 'know' about them? Is this feeling
information, or is it to be ignored as irrelevant? Putting aside whether you can prove to others you are right about that person, if you can't name the source of your knowledge (that person's pheromones? how he moves his eyes, which your instinct notes but you cognitively don't understand?) does that mean that in fact you do not know this after all? If not, what would you call it, believing it? But that sounds much too strong; if anything belief sounds like it's even harder to define in this context than knowing. And I think we would agree it would be foolish to say that you
do not have any information, because then you'd be advocating for people to ignore their instincts, which is super dangerous advice.
2) Premise: there is a God, let's say the Christian one. So you walk along, and get the notion that something would be a mistake for you to do. Along with our premise, let's suppose this vibe is sent to you via guardian angel or from God directly. It is a direct transmission advising a better vs worse course for you. In such a metaphysics (i.e. where things like this happen) what would you call that pipeline going to people and guiding them? If it's not knowledge they gain, then it's...what? Information of some kind, to be sure, but I feel like we begin to mangle language by saying you can have correct and true information and yet decline to call it knowing something. And yet under this metaphysics it will be impossible to name the source, or to articulate where it came from or to show how you know it's right. This kind of information would be bad to enforce onto someone else, but good to accept for yourself; so bad for
persuasion, but good for personal choices. So that's not knowledge? Again, calling it belief but not knowledge seems to mangle the language even worse.
3) What if our knowledge of physics is terrible right now (it is), and we one day learn that micro-wormholes connect all points in space immediately. Let's call this 'macro entanglement'. Actually this has already been suggested in physics theory, as the understanding of what entanglement even is, and what it means for remote things to be connected, is very new for us. So anyhow let's say that distance is in some respect an illusion; that all things are connected in a literal sense. If this is true then information transmission can occur in all manner of ways we don't understand at present. In fact, if it was true it would mean that our entire concept of information transmission is undeveloped to the point where it is effectively zero. So by strict standard of understanding where our information comes from we would have to say we all currently know nothing, since we cannot articulate where our knowledge comes from at a low level. We can make high-level approximations, but these could turn out to be inaccurate. And further, we may be receiving all kinds of information all the time that we cannot cognitively process. Maybe it's the collective subconscious; or the macro-organism called the human race; or the ether. Call it anything you like. Under such conditions, I would find it hard to believe that we are equipped to exhaustively say what is or isn't knowledge in a strict sense.
It should be possible to evaluate, at least in principle, the source of that knowledge. Having a source of the knowledge that you can articulate is evidence. The strength of the evidence is dependent on the source (repeatable experiment being strongest; an authoritative statement by a trustworthy expert being intermediate; source with strong motivation and history of falsehoods being among the weakest).
I get what you're on about, and I'm not opposed to what you are saying in general, but you are drawing the wrong boundary. It is useful and maybe even coherent for us to compare information sources and demonstrate that someone is basing a statement on little or nothing. "I read it on 4chan" is not a good way to source information, compared to "I used my own eyes, compared data, looked at the reality to see if my theory matches, etc etc." So yes, stupidity and wrong opinions are a thing. But at the same time while we can limit knowledge to things that actually exist and claim that someone
doesn't know what they're talking about when they have a bogus source, we cannot additionally add in cases where someone does have a legitimate source but that's it's one they cannot name and say those also aren't knowing. One fails the reality test, but the other only fails the communicability test. Failing be able to communicate something doesn't make it false. It doesn't mean we should believe the person, but it also doesn't mean we can say they don't really know it.
Going back to my point above, if people feel like they're being taken advantage of, but don't really understand the mechanisms and systems doing so, it strikes me as being a double slap in the face to suppose they don't really know anything. Not only does the system that takes advantage of them work (we are supposing) because they don't understand it - since if they did it would fail - but then to say that since they don't understand it they don't know what they're talking about when they feel they're being taken advantage of - ouch! There is plenty a person can pick up on without being to articulate it. In fact it's a good bet that the Trumpers really do have something to be upset about, but it's also likely they can't articulate what it is so will lap up some explanation given to them by a demagogue. The danger isn't that they're wrong about being upset, it's that due to lack of transparency (since the system in question works by virtue of being unseen) the systems in place make it very easy to scapegoat or misdirect.