My view is that people should be able to make remarks that are annoying to others. Personally, I think it's pretty stupid to set out just to annoy someone by making silly or rude remarks but I don't think they should be censored in any way.
I thought that the term "troll" was meant to describe people who "stalk" a person or an organisation, making false/libellous statements about them, with the intention of, in the case of an organisation, challenging them or bringing them into disrepute and, in the case of an individual, frightening, humiliating or insulting them.
Threatening someone is a staightforward crime and can be dealt with as such. To take legal action for libel is trickier for an ordinary individual because it's difficult to prove and expensive to litigate.
In the original post's link, the case mentioned is a campaign against the NHS relating to the death of a vulnerable young person due to proven negligence. Personally, I would think it totally inappropriate to try and close this down as it isn't motivated by an irrational desire to be malicious just for the twisted fun of it, but is a natural reaction to the grief and unresolved anger surrounding the death of a son.