Toss out silly ideas like the basilisk thing, and think up real info hazard possibilities.
E.g., let's say you knew what Snowden was up to, a few weeks before he figured out how to publish what he'd found and leave the US.
You'd have done a lot of harm to post that info publicly.
Suppose you find a laptop left in a taxi, with police records including personal details of rape victims in your city for the past 20 years. Post it to 4chan? Uh, no.
What about ongoing undercover investigations? Post it?
You accidentally shoulder-surf sensitive credentials -- bank manager's login, nuclear plant access code, whatever. Post them online?
Simple ways to make highly dangerous weapons, drugs, poisons, etc. can also be info hazards.
It's honestly not that hard to imagine real-life examples, without having the dangerous info in question or descending into government assassin-type scenarios.
It's just any data that, if you make it generally available, will predictably result in bad things happening.
In some cases -- like revealing important security flaws -- a public disclosure may be a last resort if less harmful methods have failed, but it's likely not an ethical first resort in those cases.
If I modded this, I would delete your post.
If I don't take info hazards as a serious threat, there isn't anything to sort those statements with.
Something as innocuous as "Think safe thoughts!" enjoys a similar property.