These people are big on being "nice", even if it's not "correct". If I said yes, and had the drink, likely they would talk about it later.
They had homemade wine at Christmas and said it would be fine if i had some. I declined. I do eat though. I'm supposed to bring my own food to eat but on my first weekend there they said "You like spaghetti? Don't bring a lunch tomorrow, you'll eat with us." lol Perk!