Ick! Both as a GM and a player, that would annoy the heck out of me.
Failure should be an option! If you pull the players around by the nose then they will not thank you for it.
A mystery is better when handled as a flowchart - not all the clues lead to the same place, and some clues can be in several areas. But do not just hand them the answers.
To be clear, I'm ONLY talking about situations where, if the party doesn't get the information the campaign grinds to a halt. If there are alternatives to not getting this information, great!
In a sandbox game, I can't imagine that there will ever be any information so important that the campaign just stops if the party doesn't get it. If it's a more linear game (such as most published adventures), then there can be information that's so important that it has to be given to the party.
As long as you can still have a fun time WITHOUT that information, then you can absolutely hide it and only give it out if the PCs find it. But if the next step after "the party fails to find this information" is "okay, well, I guess this campaign is over," then you should just give it to them rather than make it a hidden thing to find.
There are lots of times in a campaign when the DM just gives out information. The mysterious stranger approaches the party and tells them about the evil monster terrorizing villagers or what have you. That's okay. This is the same thing; it's just coming from a compartment in the BBEG's chamber rather than a mysterious stranger.
Edit: I hadn't noticed that the OP had put up the details of this situation. I'd say that this is a situation where things can continue even if the party doesn't find the information, so it doesn't have to be given out. Sure, the world might end, but it's possible that the PCs might learn the same information another way later on, which could be interesting. I'm mainly thinking about situations where the PCs literally have nowhere to go and nothing to do if they don't find the secret; in that case, it shouldn't be a secret.