By jove, you're on the right track. The Job Centre and other signatories (approved charities/local authority) give food bank vouchers to those who they have financially assessed and determined that they require an emergency food parcel due to their financial circumstances.
People can want free "grub" all they like, but unless they are deemed eligible by an approved assessor then they can't access a food bank. Even those that are eligible are restricted by how often they can access a food parcel.
Do you know what that means? It's not about the food being free, it's about you and your family not ****ing starving to death because you literally cannot afford to buy food.