"You got me a Batcave? A Batcave!"
'Leverage' - "The Last Dam Job"
"So... you built a Batcave under Alcatraz....."
Doctor Diego "Doc" Soto:
'Alcatraz' - "Pilot"
I've looked over that original article and I think the premise still holds up. Other people found their way into the Batcave, with most of them surviving the experience. (Save for poor deluded Molly who fell into the Batcave's nuclear reactor - "What a way to go-go.") And those who had been in the Batcave may have eventually told their story to the media after Batman retired.
|Molly falls to her death|
So eventually the general public would have known about it, if not where it was actually located, and so it would have been no big deal to work mentions of it into their conversation. (Back in 2009, it was also mentioned on an episode of 'General Hospital'!)
And in Toobworld, as has happened so often with other TV shows that became iconic, fictional TV shows were made about them. You wouldn't believe how many TV shows mention a TV show about Batman and starring the televersion of Adam West as well!