This isn’t a sugar free diet but a low sugar diet. Onions have 3-6g of sugar, a head of lettuce has 3g of sugar, rutabega has like 10g of sugar, etc. If you were compare this to fruits, a banana contains 30g of sugar, a green apple contains 20g of sugar, pineapple is high in sugar (40g per serving or something)…
What this diet comes down to is feeding the yeast less than your previous american style diet.
If you have an underlying immune problem, this is hard to treat by yourself on your own. This is why I recommend consulting a naturopath who can help you unravel you health history and make decisions based on this.