There’s a computer programmer in the United States called Ward Cunningham, and he’s widely regarded as the inventor of the wiki. A wiki is a source of online information that is collaboratively edited by the very people who read it, the best-known example being Wikipedia.
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Anyway, he’s a smart and inventive fellow, and one of the many things he’s known for outside wikis is “Cunningham’s Law”. It goes like this: “The best way to get the right answer on the internet is not to ask a question; it’s to post the wrong answer.”
Now, Cunningham himself says he was misquoted and that he never suggested a person should ask a question by proposing an incorrect answer. Despite his own disavowal, and the fact that it specifically relates to digital forums, I think Cunningham’s Law might still be useful to you.
At the heart of the dictum is the idea that you can entice someone who knows the truth about a disputed question – or, yes, a mystery – to reveal it not by asking directly, but by appealing to an instinct that trumps their reticence or discretion. That might be a sense of injustice or righteousness or self-regard … or simply a desire to correct the record.
Under different circumstances, such a ploy could be seen as unscrupulous or even unethical, a form of deceptive baiting or emotional exploitation. In your situation, though – and as long as you choose your statement carefully – I think we can comfortably describe this as gentle, if mischievous, manipulation.
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Nobody will be hurt by you (or another brave colleague) confidently stating as fact an answer you know to be wrong about a question that, in the scheme of things, doesn’t really matter.
It’s not a foolproof plan, by any means, but it costs pretty close to nothing, wouldn’t require much time – perhaps a meeting to get the tone and tenor of your fabrication just right – and, most importantly, could be as fun as the mystery itself.
My advice is to get creative and see whether you can tease the truth out of a stubborn hold-out with an irresistibly silly confection.