Keep reading, it's a little more complex then simply suggesting anonymity is guaranteed:
"A defendant in a defamation lawsuit attempted to use this case as a precedent that "sources have the right of anonymous speech under the First Amendment", but in 2011, the New Jersey Supreme Court rejected the argument, distinguishing that case from McIntyre."
Your second link doesn't really pertain to the topic at hand.
Nonetheless, it's an interesting concept that I'm not sure I particularly agree with.
It may not be a right, but it can help protect that freedom of speech and I think that is a pretty worthwhile goal. Also, I agree most anonymous writings don't amount to much of anything, but it doesn't mean they don't have their uses.
For very good reason, I might add.
In fact, most anonymous speech can safely be discounted as nonsense.