After my original post I called the wife, who’s out of town at the moment.
Turns out lots of food banks get state or federal money, and so they have paperwork, means-testing, etc.
But the one she’s with are run by a small church and don’t have any such nonsense.
That explains it - private charities. The food banks I was talking about are run by Catholic churches.
Also, there are other food “ministries” I know about, and no one is questioned when they take the food because they’re run by churches, too.