I’ve been eating low carb @1200 calories using MFP for most of a year. The difference between MFP and the BSD, for me, is that I drop 400 calories of fat. I still eat quite a bit of fiber (30-40 grams most days).
Formally, the BSD doesn’t restrict carbs – they are to be considered side dishes, rather than the main event, and should be made up of high quality carbs (with lots of above ground veggies & fiber and few or no simple starches). Some of the recipes in the book are a bit too high carb for me – so I still count carbs and calories to make sure the higher carbs don’t mess with my blood glucose levels.