I hope that's what the original poster who you quoted meant, because I don't see all that much wrong with the examples you mention. No, there's no need to engage people in discussions about things if it doesn't really impact them, or they can't really jump in and help the situation.
However, in the absence of some legal requirement to keep quiet, if some employee got wind of one of those situations, and came to you and asked you about it, I really do hope you'd be honest and forthcoming. Because otherwise I think that's when you'd cross the line (for me at least) into being untrustworthy.
One thing to mention though: in the case of your first example, if that huge deal really is going to fall through, no question, and the company is going to fail because of that, no question, I would lose all respect for an executive who didn't pro-actively have the hard talk with employees about that situation. Yes, some people will leave. But that's life, and your employees have entrusted their livelihood with you; you owe them that level of honesty.
> I just had to be confident that I could put out those fires, or put in place strategies to mitigate them, and let the team know it's all under control.
Which is fine! Because if you truly did put out those fires, or at least put in place some mitigating strategies, then you were absolutely telling the truth that it was under control.
> I think job #1 in management is to shield the team from distractions
The difference is that some "distractions" can have a material impact on those employees' lives. An executive who hides those things and lies about them to employees is not worthy of respect. For "distractions" that truly are just distractions, sure, fine, no need to broadcast.
But I think a key question is: if a bit of news could make a reasonable employee, thinking logically about the news, decide to quit, then... you absolutely should be disclosing that news. Anything else is just a betrayal of the implicit trust an employee must have in their employer.
And yes, I know all this might seem pretty idealized, and I know there are a lot of companies and executives who won't get these things right. But that doesn't mean I want to work for those people.