Ali,
You 
don't need to eat carbs (particularly of the sugary/starchier varieties) 
 unless you choose to.  But the less of them you consume the more likely you are to reduce your glucose levels, and, if  needs be, reduce your weight.  Your meter will tell you which and much much of them 
your body can handle. So this together with your food preferences will help you find the right balance of different types of food for your requirements.
If you are going to go on a  low carb high(er) fat diet you will be (in part at least) replacing  carbs with fats for energy  - you don't need the carbs and  the advice to eat them in the form of vegetables is 
not because you need them but because you need the nutritious stuff in the vegetables - unless you're going to replace these  in the form of supplements 

.  So on a  low carb diet you opt for the better value foods and  choose vegetables, some fruits, and nuts for your preferred carb sources.  
Bernstein is probably an extreme example,  but his intention is to  (try to) make sure his patients/followers have as close to normal glucose levels as their non diabetic counterparts, and still maintain a healthy diet.
Robbity
PS I thought it might be helpful add a bit more personal information re carbs;  From choice I'm on a very low carb/ketogenic diet (lower than 50 grams of carbs a day), and as such my main energy source is now coming from fats/oils in my food.  So any carbs I eat  are "incidental" and  I no longer need them for fueling my body - they just happen to come from foods I eat for other reasons - 
not because they're carbs and I need them in my diet.  So most of my carbs are non starchy/sugary ones and come from vegetables, fruit, and nuts.  
.