Having never been there, I don't know the variety of foods they have. I would hope the OP does know all that they have, to make SURE the child wouldn't eat anything.
That said....
I'm just glad none of mine were picky. I think it would be an easy problem to solve though. It would take about one day.
It's obvious you have never encountered a TRULY picky child. All of my sibs were absolute nightmares at the table. ALL of them would, and did, starve themselves if there was nothing they could/would eat. Countless hours were spent at the dinner table, as food went cold and tempers got higher. A certain big sister, one night, couldn't take it anymore and ate her younger brother's potatoes just so they (yes, they were BOTH kept at the table b/c of ONE person) could get up.
My full brother (about whom I know the most, food-wise, because I lived with him) would go a whole day without food if he was given the wrong thing. I despite PB&honey and he hated PB&J, and the one day our lunches were swapped, I choked the PB&honey down and he came home with the full lunch intact.
(and now I'm the one with some random food and many environmental allergies, and the siblings have NONE...who made the right biological choice, I ask?)
Picky is one thing, having a disorder is another...
I don't know that my sibs have disorders, but they Would Not Eat it if they didn't want it, and from that lesson, with my own son I've tried hard to honor it. Thankfully he's been more like me, and his palate often accepts things his nose or eyes said no to.
(another picky moment...my own mom was forced to eat all food given to her...every time they had beef, she ended up throwing it up...her father ALWAYS forced her to finish it, even though he knew what was going to happen... I'm still not sure how that was less wasteful than just saving that beef for lunch or something, but it was what her father insisted on!)