I can see that happening... whenever you eat anything your body releases insulin, whether it's carbs or not, and if there aren't any carbs for it to work against, that can probably lower it too much (especially if you are on any medication).
I do get into the 70s when I go extremely low carb, so I still have a couple servings of carbs a day. I just make sure it's no more than 15g at a time and pair it with protein so I don't get a spike. But I'm nursing a baby, and that has an effect on my blood sugar.
That's the thing with this disease... it's different for everyone.