Thanks for clearing that up for me. Seeing the ads on this website got me wondering.
As Myth points out, Bernstein's diet is not Paleo, but you can easily follow his carb restrictions with Paleo foods. Avoid soy, low fat dairy, and artificial sweeteners. Eat real, whole, organic and pastured food, stick to natural fats and don't limit them. Your results will be great.
Bernstein is a product of his time, when GMO and pesticides were less prevalent, fat was (incorrectly) identified as the enemy, and soy was the miracle food. We know better now, but Bernstein--in his 80's now--didn't update these recommendations in the latest edition of his book as he should have.
If you only follow the meat and veggie recommendations then it could be an extremely restricted version of a Paleo lifestyle. The diet as a whole is not Paleo because he recommends products like artificial sweeteners, diet soda, fat free/low fat dairy, sugar free jello, soy flour to replace grain flour, margarine.
Dr. Bernstein's main goal is very low carb for diabetics.
If you want to simulate something like that in a Paleo lifestyle fashion, I recommend doing a low carb Whole30 and seeing where your needs are from there.