"Milk products" may include kefir, yogurt and other fermented dairy foods that do not contain lactose. There are many other vegetables besides legumes and those that contain lots of starch.
HV's approach to contolling candida is based on increasing fiber and probiotic consumption. The SCD is headed in the right direction, but does not go far enough. You want lots of added lactic bacteria, and plenty of fiber for them to feed on.