I think it acknowledges a simple truth:
We all make mistakes. Some of them stunningly big and we think - even for a moment - "my boss is going to fire me!" And then once we calm down, we stop to think about what happened, how to fix it, and how to prevent it from ever happening again.
And if you claim to have never made one, you're either a) lying, b) oblivious or c) so green that you'll make those mistakes with me. The first two reasons don't fly with me.
Long story short, I cornered that director some time after the meeting, apologized profusely, and explained that I'm overly sensitive to mistakes in this position since I witnessed first-hand what happened when a predecessor of mine made a "simple" error, which resulted in a major patient-impacting event (which resulted in an FDA investigation). The upshot is that this director, from that point on, trusted me more than anyone else on the team (even though I was "highly insubordinate" in the previous meeting).