Asklemmy

I manage a team and came to say this same thing. If the topic is a lesson the whole team can benefit from, I bring the whole team in. The more obstacles that can be resolved without my involvement the better. Sometimes that means bringing the whole team in on a mistake, too. I do my best to ensure it's framed as simply as that though. A mistake to learn from. As well as ensuring the employee is in a good headspace to share that moment. It's not a punishment. Mistakes happen.

This may not be the case in your situation, but something to consider.

I think the problem op had with this situation and boss' approach was that it definitely had shades of admonishment, or at least potentially so, hence wanting to know op's the thought process. I don't manage people professionally and never have so I'm not speaking from knowledge of best practice, but I do know that in general this isn't going to be conducive to good outcomes. Necessary or otherwise, if admonishment or at least finding of fault with the behaviour of the person is on the cards doing so publicly is embarrassing and unlikely to foster the goodwill required for that person to think or behave differently since it moves the whole situation out of the framing of learning a lesson about how to do your job in future and in to something adversarial, with the boss now a malign influence to be resented or feared or both and the humiliation in front of peers now also means that person is more likely to feel isolated from them too with their peers are now to be viewed with apprehension as well as the boss. It's hard to work well and to avoid making mistakes with such factors at play. One such occasion alone, probably not, but if it's something boss wants to do a lot as a general management strategy, it's hard to see that going well for anyone involved.