Hahaha they are not starving if they have eaten a palm-sized amount of food. That's like half an apple.
Just reminding people that there are a LOT of empty calories to put in your child's face at Disney, and people often forget that kids cannot readily consume the volume of food nor the calories an adult should be. One handful of popcorn can distract a small tummy that it needs to eat a sandwich, especially when, "LOOK KIDS! MICKEY MOUSE is on that parade float!" an hour later you see an exhausted mom glaring at her toddler who won't touch his plate of buffet food because he knows in ten minutes he can sucker Grandma out of some Goldfish crackers she has "just in case".
Don't manipulate them and don't let them manipulate you. As I said, parents provide WHEN and WHAT is being served. Children decide WHAT and HOW MUCH to eat. They can't eat the chicken nuggets if they aren't any to be served. If it's not a mealtime, they shouldn't be eating a snack. vacation or not! Nothing snarls up a vacation more than a child with a disrupted routine to their benefit - you get them back home and it's another battle to reinforce the normal routine again. I'm not well-rested and refreshed after a week of trying to re-set the sleep schedule and arguing about what we don't get when we are not on vacation... I don't wish to make that worse!!! LOL