to expect pre-school not to let my ds be hungry all afternoon?

[Bambiraptor]

My ds has just started pre-school and stays for lunch every day. Two days a week he stays until 3pm while I am at work.
He is a very fussy eater and the lunches that are provided are so far not going down very well.
Today, as he was staying until 3pm, I put a sandwich in his backpack and asked the staff to give it to him if he didn't eat his lunch, as I didn't want him to be hungry all afternoon.
They have refused however, saying that it will not encourage him to eat his lunch if he knows he has an alternative.
They are right of course, but surely that is my problem not theirs and they should do as I ask.
So AIBU?

Hi essbee!! Of course, parents/siblings very welcome to stay/eat/join in etc - the invitations just indicate who gets a party bag (mutter mutter, decline of western civilisation) cos I've only got 20 of them. Fennel et al are staying, and there will be wine

The bottom line is I don't want ds to be hungry all day. I am going to see if the staff will give him his packed lunch on the 2 days he is there all day, and let him try the school dinners on the other 3 days.
That should be an acceptable compromise!

mm22bys, there is only one food option. They don't have a choice. The food is nice healthy food.
However it could have 2 Michelin stars and ds would not eat it if he didn't like the look of it.