How does it beg the question?

There is no truth being asserted in the premise causing the conclusion to be true. It's fairly clear that it was a statement from an original source, that source being trustworthy is where we would find (or not find) the information which would show the conclusion to be true, not the premise of the 'fantasy.'

Give it up. In 30+ years of learning English, the only times I've ever seen it used in that sense has been when someone is being a pedant on forums and illustrating the now rapidly outmoded meaning of the phrase.

In 20+ years of learning English I've heard it used several times to refer to an obvious question or lack of information

"$noun did $verb which resulted in $result and $result is $something interest which begs the question $question."

well, your confusion of tenses kinda colors your knowledge about grammar rather questionable and i say that as a foreign speaker

Until it changes meaning, I cannot give it up. A curse I tell you!