In all fairness, low carbing can cause low levels of potassium which is why in the initial stages a potassium supplement is recommended, although it's often not necessary if you are eating veggies from the allowed list other than lettuce. Broccoli and spinach are both excellent sources of potassium. Low carbing is not known, however, to cause dangerously low levels of potassium. Diuretics can. Just because she wasn't talking about being fat doesn't mean that she wasn't using a diuretic to help speed her weight loss and it's very unlikely that she would have shared that information with her parents. Teens do some dangerous things on the recommendation of the friend of a friend. Given her sudden collapse, I'm very surprised they didn't do a drug panel in the ER to find out if she was taking anything that could have caused her condition.
The statement that low carb diets cause muscle breakdown is absolutely false. If you are consuming adequate amounts of protein the body has no reason to break down its own muscle mass for the protein or energy that it needs. For energy it will go to its fat stores first.
As for the dehydration, nausea, weakness, etc....yes, those sometimes do happen in the first few days due to carb withdrawal (why do you think it's recommended to drink at least eight 8 oz. glass of water daily?).
If low carb was to blame for this (and I'm not saying it is) it's because this girl was doing her own version of it without any research as to what she should have been doing (note: had she been eating the veggies, it's unlikely she would have had low potassium and had she been eating cheese and/or cream, low calcium would have also been unlikely) and possibly taking things that don't mix with low carb or starving herself.
Low carb without sufficient water, veggies or supplements is not Atkins. As a matter of fact, it's not any low carb plan that I'm aware of.