There's a very similar case going on in Sweden right now. A couple who lived an "alternative wellness lifestyle", didn't register their child's birth (which they are legally required to do) and was "distrustful" of the Swedish authorities, fed their child a "vegan diet" consisting of breast-milk, brown rice, vegetables and fruit.
At the age of two their child was almost about to die from nutritional deficiencies when they were brought to the hospital, apparently only surviving because of the emergency response. The parents on the other hand maintain that their daughter had serious allergies and they had problems finding a appropriate diet for her, and that her issues were caused by gastroenteritis over 4 days. I should note here that it's not possible that to get nutritional deficiencies that are life threatening over 4 days.
The fathers motivation for not registering the child's birth was that "Because I believe that Sweden as a state should not be allowed to own her and take loans in her name". When questioned whether they received any nutritional supplements or anything similar he responded with: "No, nothing like that. She gets sunshine, laughter and hugs."