We all err at one time or another.
Children in school err too.
When children make mistakes, it's good to talk it over with them and redirect. In fact those errors at school in a safe place are a good way to learn about right and wrong.
Sometimes students, parents, and teachers don't own mistakes. They may not want to own that their child, student, or they themselves misbehaved in some way. In most cases that kind of denial leads to bigger problems. For example as I've watched children over the years, those that don't reckon with behavioral challenges big or small in the early years tend to have bigger issues later on. It's best to own up, face the consequences, and learn about safe, positive behavior when you're young rather than reap the much bigger consequences of behavioral issues later on.
Now this is not to say that we shouldn't review all aspects of misbehavior. Sometimes children are unfairly judged or accused and that's not right. At other times expectations are not developmentally correct leaving little room for children to be children. Too tight rules and parameters off invite misbehavior rather than prevent it.
In the best of circumstances, we have to be cognizant of children's behavior throughout the day. When errors happen, it's best to talk the situation over with the children involved and also to talk it over with their parents. We have to work together--students, colleagues, and family members--when it comes to coaching and caring for children. There's no one answer except for working together to do everything we can to support children well.