I just can't get over the fact that the poor kid probably doesn't even know what the word "dinnertime" means. Unless meals at her house are different than Grandma's, she may have heard something like "No, I won't make you a sandwich because Blah Blah Blah."
I know parenting styles are different and the kids actually are fed, but the idea that Grandma will not feed you unless you specifically ask for it, upsets me deeply. Kids should not have to be in charge of their own meal planning. I know to some people it sounds indulgent, but to me it sounds like Oliver Twist.