But there's something to the status thing, and I think he illustrates it: if you have any status or credibility at all, you also have the ability to set the tone.
And you probably should. The few managers and executives I've met with who can't take "I don't know" and "this was a mistake" in stride without losing their cool immediately start getting lied to and shielded from bad news.
My personal anecdote contrary to your point is my first programming interview. My answer to pretty much every question was "I don't know, but I'm excited to learn". I thought the interview went horribly, but I was offered the job. The owner who hired me (who ended up becoming a friend and we worked together at multiple companies), told me later that my confidence to say I didn't know something is what put me ahead of other candidates. Without knowing me well yet, he felt he would be able to trust me.
My take was that you can be confident about the skills that you _do_ have, and honest about the skills you _don't_ have.
Then we would schedule their termination.
If you are already viewed as an alpha intellect in the group (or say you are viewed as one of the best software engineers in your company), then you have the luxury of being able to be modest and in fact expressing such modesty will even enhance your reputation among your peers.
If you are somewhat insecure about your abilities or if your reputation is unestablished or you are not particularly recognised, then admitting ignorance in front of your peers is unlikely to enhance your reputation or feeling of self-worth.
When I hear those at the top-of-the-hierarchy - whether in a management structure or in "technical ability" structure - being modest about their abilities or admitting ignorance, it often comes across as insincere to me.