AmyRose...I was one of those kids. When I was little, I was chubby and at that time, doctors still believed that sugar and bananas made you fat so...I was denied ALL sugar and NEVER got to eat a banana...things that I really liked. Yup...I rebelled at the first opportunity and bought stuff that I had been denied all those years as soon as I had my own money (allowance or babysitting). Knowing that I would get scolded if either of my parents saw me eating those things, it also taught me to hide those treats or binge on them so that they were gone by the time I was picked up from school or got home. Of course, the other dynamic there was that my older brother was very skinny so my mom bought all those sugary treats for him so he could gain some weight and I was never allowed to eat them.
Different kids will react differently to restrictions such as that and I think a lot does depend on how it is presented to the child and whether it is applied fairly and evenly to everyone in the home.
With my girls I don't tell them that foods are "good" or "bad"...it's more an issue of "good fuel" for their bodies or "junky fuel". Just as cars run better on the right fuel, so do bodies and that's an analogy that they understand.