my understanding of the alcohol and ketosis thing is that it is because on a vlcd like cambridge you do not replenish your glycogen stores to significant levels. Your brain's major source of energy is glycogen. Therefore the small amount of glycogen we produce from our packs is used mostly by our brain. There is something about that small amount of glycogen, it being the brain's main source of energy, the effect of alcohol on the liver when in mild ketosis that is behind it all (I can never remember the detail of things after a few months).
Anyway, with Atkins a person can eat loads of fatty foods as well as protein. Therefore, the individual is constantly restocking their glycogen (fat that is not immediately absorbed by the body is converted to glycogen and stored by the body).
That is why you are advised to avoid alcohol on vlcd but not on Atkins - because on Atkins the amount of fat you are eating gives you a higher level of glycogen stores in the body