When you phone into a Radio 1 show to say you don't like the pop star they've got live in the studio with them, you don't expect said pop star to sneakily write down your mobile phone number, take it home with him and start sending you death threats. Yet this is exactly what happened last week, after Dappy from N-Dubz, an urban group who sell by the bucketload to the ringtone generation, took umbrage at a Lincolnshire woman calling him "vile" and "a little boy with a silly hat". According to The Sun, which reprinted his text messages, he told her she was going to die, called her a lot of names that they replaced with asterisks, and said that she would never be left alone until she apologised, which she refused to do. The 22-year-old Anglo-Greek rapper and songwriter, real name is Costas Dinos Contostavlos, has apologised to her.

Once I'd got over the concept of disproportionate response being taken to such dizzying new heights by a man who calls himself Dappy, and the immense irony of, well, all of it, I have to say I was left thinking the bloke had a point. Grow a thick skin, everyone has said to him, meaning, be immune to criticism. Remain impervious to what people say about you. But what's so good about thick skins? So people can carry on insulting you while you swallow your tears and pretend not to care? Isn't it thick skin that means a million people can march, the biggest public gathering in history, and the Government can sit there unmoved and head into an ill-advised war all the same? Don't thick skins grow on the same heads as deaf ears?

Dappy burst through the fourth wall of celebrity. He's broken down the unspoken contract that says: you are rich and famous and on radio annoying me, and thus I have the right to call you things that I would never say to your face. The Sun quotes her as saying that "his behaviour is unprofessional", as if being famous was a profession that came with its own code of conduct.

People feel they can be as rude as they like to published writers, simply because they are published writers. One journalist I know wrote an article about music and nightclubbing to which an online reader left the comment – easily offended readers should skip the next two three lines – that he wanted to kick her in the cunt so hard that she choked on her uterus. This comment-leaver turned out to be a music blogger known to some, not a random psychopath. What surprises me the most about the bottom half of the internet, that place where all the angry comments go, is that so many of the people writing them turn out not to be rabid murderers but ordinary mild people who casually fire off drive-by verbal shootings in their lunch breaks.

Some fellow journalists told this writer not to worry about it because, you know, come on, sticks and stones, you'd be silly to let such comments affect you. It's only words. But if words can't affect you, then what are we doing trading in them? Giles Coren knew the currency he was dealing in last week when he twittered his proposal to fuck, kill and burn his neighbour's 12-year-old son.

And although Dappy's response went too far and was creepy and disturbing, there is something touching in a man who has sold a million records and has legions of adoring fans actually caring about one woman not liking him. Part of me wants to applaud him for giving a toss. For not being so megalomaniac that he can't even hear her. Thick skins are for elephants who spend all day in the sun – not The Sun.