I am very grateful to Dr. Bernstein for his book and advocacy of a low carb and healthy diet. Others, including non-diabetics, are coming round to advantages of this kind of approach, too.
I eat more than 30 carbs per day, but adhere to the kind of foods he advocates - it is not only nuts and spinach! In fact, he recommends that nuts be eaten sparingly if at all (as it's hard to stop, once you get started, a fact which I can attest to).
My A1C is coming down, little by little, and I'm now at 6.3. Pretty good, considering that my pump has let me down with non-delivery of insulin at regular intervals.
But just like you, one of my nurse educators looked at me very sternly when she noticed I was light on carbs. I lost a lot of weight when I came down with Type 1 very suddenly. However, my weight is just about right, now, so my medical team are quite approving of that.
They have been impressed with how even my blood sugars have been over periods of time. And I have not been starving myself, but adhering to Dr. Bernstein's advice on what is good for us, and avoiding what will cause spikes in BGs. It's the spirit of the advice, rather than the letter of it that I follow, and it is immensely helpful.
By the way, my last LDL was 83, I think, and HDL was off the charts - over a 100, so my Primary Care Practitioner gave up on her insistance on statins for me! It will be interesting to see if yours improves if you adhere to his advice on lots of green veggies!
Best of luck!