I believe there's a fair bit of evidence to the effect of, any "diet" that restricts one's food options - be it calorie restriction, low fat, low carbs, low pro

I believe there's a fair bit of evidence to the effect of, any "diet" that restricts one's food options - be it calorie restriction, low fat, low carbs, low protein, intermittent fasting, no sugar, whatever - will result in weight loss as long as it's stuck to. Which makes sense logically; if normally you'd eat whatever you felt like, and then you restrict what (or when) you're "allowed" to eat, some substitution will be done, but you'll likely also just eat less. And then when you go off the diet (either intentionally, or more likely, by just slowly drifting back to the norm), you'll return to eating what you were before, and will return to your original weight. Which is why the only diet that works is one you can stick to indefinitely. So, if the parent can stick to a no fat, high complex carbs diet for life, it will probably work for them.