Indeed. The GA Court of Appeals did not say that (quoting TFS) "Parents can be held liable for what their kids post on Facebook." What they did say is that the parents' 11 months of inaction, after they were given notice of their son's defamatory FB profile, could constitute negligence. A reasonable jury could possibly find that not telling your kid to take such content down was negligent, and it's a question for the jury. Thus the subject matter of this case is on the internet, but it's not really about the internet. The parents could be liable under the same theory if they knew their son was handing out flyers with this defamatory content and did nothing for 11 months.
For those less acquainted with the trial process in the US, this appeal by the plaintiff parents (of the defamed girl) was from the trial court's granting of summary judgment in favor of the defendant parents (of the defaming boy). This is type of motion usually happens before any of the actual "trial-y" kinds of things like impaneling a jury and witness testimony, and it's based only on each side's contentions and the undisputed facts that both parties have agreed on. The defendant parents essentially argued, "Based on all the facts we stipulated to, and looking at the plaintiffs' assertions in a light most favorable to them, they still can't win. Even if what they're arguing is 100% right, no reasonable jury could find against us. Judge, can you just end this thing now?"
Specifically, here, it appears they argued something like "The defamation occurred when junior posted that stuff, and we had no actual knowledge, nor reason to believe junior would do such a thing, until after the school told us--long after the defamatory act!" And the trial court judge said, roughly, "Yup, I'm not even going to let a jury hear this, no jury could find you liable for what your kid did. Parents aren't vicariously liable for their kids' torts, etc etc."
The appellate court said, in response, "Um, yeah fine, you're not on the hook for the acts that occurred before you knew. But after you knew, you did nothing to stop it or even inquire into it, and the defamation was ongoing that whole time. This is not an automatic slam dunk for you, defendants; you need to present your evidence and arguments to a jury."
Note that at the actual trial, the parents may be able to present a decent argument for why they didn't do anything (which behavior was very curious to me). Maybe the parents are luddites and they asked their son if he ripped all the bad pages out of the Facebooks and flushed them down the interweb tubes, and he said, "yeah sure." I don't know, but those are the kinds of factual arguments they'll have to make to a jury to explain why they let this go on so long after they knew.