In it's simplest form.
You're looking at a black swan. One person says it's a black swan. The other person says it's a white swan that is painted black, but cannot provide any evidence whatsoever to back that claim up.
Who are you going to believe?
the word "unfalsifiable" seems valid here. The quickest and laziest solution for me would be to just shrug and find something else to do with my day.
The better alternative, however, would be to take as much time as needed to research the subject via credible sources who have the tools at their disposal to back up their claims (zoologists in the case of this analogy).
Then there's the two mid-way solutions: one where you do a little bit of research, accept that you don't have all of the answers you need and just go for a walk/watch telly/some other mindless activity to keep yourself busy.
And the other is where you try to fast track the necessary studying by believing that any experts on swans are liars being manipulated by an authority with a hidden agenda, then try and push this idea onto everyone else without backing up any of the anti-black swan claims thus creating a situation where you've got people siding with you based on nothing but a combination of faith towards your claim and a distrust in authority.
You can also throw in some grains of truth, maybe one, or even a group of the zoologists was given a research grant that they instead spent on an expensive boat thus showing that zoologists aren't 100% trustworthy, however, all this really proves is that said group of zoologists let their greed get to them, it doesn't prove any of the zoology related claims wrong or even that
all zoologists are untrustworthy. Even if someone with the capacity to paint a white swan black used a black swan to justify a war in the middle east (whatever the mechanics of such a process would be) it wouldn't prove that they painted the white swan black, it would just prove that they could. I could eat 1000 doughnuts and get fat, that doesn't mean I
did eat 1000 doughnuts and got fat (as fun in the short term as that sounds).
The problem with using fear over evidence is that you wind up making people feel scared about something they might not have to worry about. I see this all the time when people worry that their local active volcano is going to erupt despite the predicted margin of the eruption being anywhere from the next few minutes to the next few centuries. Could the volcanologists be lying about the margin? Sure, but that doesn't mean they are. Would it be convenient for them if the volcano erupted minutes after they just said it seems unlikely? Yes, but sadly nature doesn't take sides otherwise the volcano would've tried extra hard not to undermine the volcanologist but waiting a few centuries before erupting.
I'm going to make a bold claim knowing that my deeper knowledge of the English language isn't that great, but I feel like there is no such thing as an "expert" in any subject. We as a species can make educated guesses about what will happen and the chances of it happening will increase in percentage if the educated guesses are based on solid evidence, but there is no way to know when the unexpected will happen or how it'll happen.
This next part might sound unrelated but there was an interesting coincidence that happened to me recently. I was creating characters for a fantasy story and one of them comes from a race of blue amphibious dragons that live by the sea. I noticed after drawing said character that she looked like one of the Na'vi from Avatar. How did I fix this? I changed her colour from blue to teal....shortly afterwards hollywood released a trailer for Avatar 2....which featured teal Na'vi....that are amphibious....and live by the sea. Now I could say that James Cameron decided to hack my iPad and steal from my project that's unreleased to the public. Or even suggest that one of my friends has secret ties to James Cameron, but as tempting as that is it's more likely that we both saw teal as being a very "sea-like" colour that's pleasing to the eye. Also, while my mates are incredibly creative types I highly doubt they're sitting around drinking martinis with James Cameron and then living in a relatively cheap and basic house just for the sake of fooling little ol me.
What i'm getting at with that last paragraph is don't underestimate coincidence.
Sorry if I went off topic, it's easy for me to go on tangents with subjects like this. I'll probably review this reply later when i'm less tired if it doesn't get deleted by that point and make the necessary edits.