Did they engage in defamation? Yes. Is defamation legitimate grounds for suspension? No.
That is untrue. It is absolutely grounds for suspension. I was a high school teacher for five years and dealing with discipline amongst the students is paramount
As another has commented, if the defamation occurs on school grounds, while the student is in your charge, suspension might be appropriate. If you wish to have the authority to impose discipline for a students actions, you have to be prepared to take the responsibility that goes along with it.
You are free to pursue civil charges against the student (and their lawful guardian), but you are not free to insert yourself into such actions.
As a teacher you've got to stand in front of 30 (ish) teenagers and teach. Many of them don't want to be there, some of them have decided that they hate you personally over some personal slight from six months ago (ie: telling them they must complete their assignment rather than playing flash games, or it seems an issue with uniform as in the article).
And if you are not prepared to handle it or incapable of doing so, you are in the wrong profession. What you describe is specifically related to your ability as a teacher.
Inside or outside of school is irrelevant (though is it the case that the speech that is accessible in school is speech in school?)
It does not matter that the "speech" is "accessible in school (although your school might want to look at it's policies), it is that it is not expressed on school grounds.
Leaving discipline choices up to the good parents is fine, leaving discipline choices up to bad parents is disaster.
And who left it up to you to decide who is a good parent? Do you have that list of qualities to judge by? Or are you just advocating something similar to Mr. Justice Stewart regarding pornography: "I know it when I see it"?
At the end of the day, the punishment of suspension is about teaching them right from wrong, and a page calling your teacher a pedophile is wrong.
You seem to think that your job is simply teaching morals. Your job is not to decide what is right and what is wrong (especially when the conduct is out of your sight and control). You are not the keeper of the compass.
If you are wronged in any fashion, there are legal remedies. You seem to advocate bypassing them and acting as the arbiter of morals, even when you are not given such authority.