Not sure about other parts of the country, but our food banks don't actually work directly with individual or family clients. Our food banks only work with other non-profits that distribute the food to their client base.
I am not sure if that would complicate the issue. You would hope the non-profit organizations getting the food from the food bank would be able to evidence their clients are LMI.
_________________________
Societies that do not find work in and of itself "pleasing to God and requisite to Man," tend to be highly corrupt.