Should Schools Discipline Students for Cyber-bullying that Occurs Outside of School?

Just finished reading the New York Times article "Online Bullies Pull Schools into the Fray." If you have kids in grades 4-9, I strongly recommend that you read this article. But be forewarned, it will leave your head spinning. The examples of cyber-bulling via cellphones and social media sites, such as Facebook, Formspring and Youtube, are mind-numbing and disturbing. You are left saying, "How can kids be so cruel?" ... and ... "Maybe I should monitor my kids texts and Facebook pages more often."

But the question this NYT article raises is not about internet safety and monitoring but rather how and where should the bullying harassment be handled?  When kids do cyberbullying outside of school and the school learns of the altercation, should the actions be punishable at school? Talk about gray area. As with so many parenting and teen and tween topics, we are asking the question: where do you draw the proverbial line? You can't deny that if someone sends a nasty text away from school, that there is slim chance that the parties involved will set their differences aside when the walk through the school doors. The hurt will percolate and fester, and eventually a teacher, guidance counselor or principal will hear about it. So, then what's a school to do? We count on our school administrators to promote a safe environment for our children. Isn't anti-bullying part of that? 

What is your take ...  when it comes to matters of extreme cyberbullying (that happen outside of school but spills over into the school day) is it the principal's or school administrator's job to play judge or prosecutor?  Would love to hear your thoughts on this complex and unfortunate question.