I agree with lingerlizzie in that they are the boss of their child. It may be a phase but you have to respect their wishes as to how they are going to raise their child. It maybe that someday they will ease up but let's face it, if you give a child one piece of candy they are going to want it more and more. The child is young and I can understand at this point they are being cautious, careful parents. Wondering, is this their only child?
I also agree, everything in moderation but that can be difficult with small children, one little piece of candy they will want more.