haha I have read that article and I would suggest she doesn't know what she is talking about.
http://psychcentral.com/ask-the-ther...s-and-cutting/

It is of course possible to cut a vein, by accident or not, when cutting. I never have done but I have always worried about going too deep. But I am not afraid of *dying* through a cut vein. As far as I know from my very little first aid knowledge, it would take a very, very, very long time to die from a severed vein. Why? Because it's not an artery, and arteries move blood around the body in a major way, eg from from the heart to the head, and since the heart drives the blood in arteries, and since they are, to my knowledge, wider than veins, it's easy to die from severing an artery, it can happen in minutes. Cut arteries need immediate emergency attention, you'd know if it's an artery because the blood would spurt (bit like it does in horror films).

Ok I have just looked up first aid and it says that cut veins tend to collapse in on themselves which helps to stop the bleeding. It's a steady flow of dark blood. If it hasn't stopped after ten minutes of direct pressure, you should go to the ER. Some of the larger veins apparently don't stop bleeding by themselves so you'd need treatment for that. But as for being 'liable to lose your life because of it', well, I'd say not unless you were doing serious deep cutting and getting the arteries (or not getting treatment for a vein which doesn't stop bleeding).