I volunteer at a food pantry and a soup kitchen, and neither of them does any means testing at all. No paperwork, no questions other than the food pantry asking how many people are in your family so they know how many boxes to give you. Each box is ~30lbs of food. We give out rice, beans, canned veg, canned meat, and in the summer, some fresh fruit and veg grown on some land the church owns. We used to give out a lot of potatoes, but then the guy we were getting them from decided that selling them to the pig farm was a better idea then giving them to humans in need.