As someone who has a couple of decades of zero sugar fasting, strict paleo, and ultra low calorie dieting under his belt, this isn't true. There's nothing just fine about what happens when muscle glycogen depletes after several days of true zero carb dieting.

Even strictly cutting out starch becomes problematic after some time, though my experience is also that humans will get unique health benefits from doing that for stretches. Which avoids the trouble of all-in zero carb.