If you are in the US, the kids just got back from the Thanksgiving holiday and many were no doubt exposed to the start of holiday mania here.
On the one hand, she put all the kids in the same boat. Without a doubt, the number of instigators of the unacceptable behavior is small, but the teacher is making it clear that it is the responsibility of every student to comport themselves to meet her expectations. From certain words, "warning stick" and "gumball machine," it would seem that these are very young children. Let's face it, little ones are easily distracted, tough to settle down, and are at the point of learning impulse control.
If she had gone into detail regarding the unacceptable behaviors, the children would have all been pointing fingers......after all, my child is a well-behaved angel and said it was (pick a few names) who were bad. It could be that she sent personalized emails to the parents of the clearly guilty parties and the generalized email to the rest. One kid may start something, but even the most well-behaved at that age can be inadvertantly drawn it to it.
Sadly, it will be the responsible parents of the well-behaved children who will have the "talk," and the parents of the miscreants will just blow it off or start blaming everyone else.
What I wouldn't do with my child if this were my situation, would be do a "Sherlock Holmes" and conduct an inquiry of my child to try to nail down what happened. It won't go anywhere. I'd just have the talk as requested.