Why is it that the term "Kids will be kids" when used in these types circumstances are usually stated by the trouble makers parents? This is the attitude of the bully's parents in my cul de sac for sure. It is NOT my attitude, and should not be Carte Blanche for kids to pick on others and behave badly towards them. If I was the parent in the OP's situation I would have done the same thing, hopefully not screaming, but my voice would most definitely be different than my normal speaking voice.
It really surprises me with all the post here stating they would be very upset with the parent correcting the pushing boy. I must be crazy, because I would be upset with my child who was doing the pushing.
I don't think that's what people are saying. I think they're saying that it is not unheard of that preschool boys sometimes push, it's wrong, and they need to be disciplined. However, this doesn't mean they're going to end up juvenile deliquents. As adults, we can discipline without yelling loudly at children, especially a stranger. Is it okay for an adult to tell a child to stop doing something wrong? Yes. Is it okay for an adult to yell, in a threatening manner, at a preschooler? No. If the teacher yelled loudly at the child, everyone would be up in arms.
I must have missed where she "signed him in"

