Common household bleach, otherwise known by the brand name of Clorox is good for both a disinfectant and sanitizer. And it's EPA approved and at the proper dilution levels it even tells you on the label that it is safe for dishes and utensils and other things you use with food.
Not certain why the caution not to use bleach. However I will agree that hydrogen peroxide generally works best between the two for mold and mildew. Especially on porous surfaces.