I would need to see the actual data on that because that is definitely not my experience with social programs in the US. There is money in the federal programs for the US even not counting private organizations and states.
You don't actually have to provide income information when you first sign up for commodities programs these days (it is required later), and EBT provides a fair amount.
Shelter is the bigger concern than food for US poor. We really need to look at the whole idea of housing. Training money is there, but its pretty useless without proper shelter and transportation systems.