Here's the thing: the vast majority of a given food bank's clients are housed. Maybe not luxuriously, or even adequately, but most do have kitchens, or at least a minifridge, microwave and/or hotplate, and thus will have things like can openers, and some basic cookware. Many of them work full-time. Many are eligible for, and receive, SNAP benefits—which means they are able to buy some food, and are using the food bank to supplement that.
Very few clients are totally dependent upon a food bank in order to stay fed, and if they are that bad off, they really need to be helped to get other forms of assistance available to them (and the better food banks in larger cities have resources available to do just that).
Homeless people often have other options available, such as soup kitchens and other outreach groups that can provide them with food (and yes, most of them own can openers).
On top of that, food banks vary considerably in the quality of their offerings. Many of them out here on the West Coast coordinate with supermarket chains, restaurants, and produce wholesalers to direct edible food that would otherwise be thrown away to food banks, so fresh produce, bread, meat, dairy, and eggs are available. Even the smallish town nearest to me has a decent selection of fresh food; it's not just dry staples and canned veg, like it used to be (and, in some places, still is).
I don't know where the food bank was where this woman Kelly's quoting allegedly talked to the clients and asked them what she should donate, but it sounds like a pretty shitty one. And if she's really that fucking concerned about food bank activism, and wants to lecture everybody else about what to donate, she really should try volunteering at one for a while. Most ask for two to four hours a week, on a six-month committment; it's a real eye-opener (in both good and bad ways); and, unless you're a special kind of asshole, you end up making friends with some really amazing people. But I doubt that's ever crossed her mind, and it sure as shit isn't on Kelly's radar.