they had no place to store a case of tomatoes, or cauliflower.

It wasn’t homeless or starving people turning it away. It was other organizations that didn’t have the space to store it. Probably because their shelves were also full of food that they need to give away before it spoils.

storing it is their main concern

… How exactly do you imagine this works? How do you accept food that you can’t put anywhere? Let me guess, you think they should just bring it to the homeless? Well:

Word got out that we were loading up my pickup with food and taking it to the homeless camps. I did get a number of them to start coming to the bank to get food. But it was easier when I could take stuff to them.

He literally can’t bring the food to the starving. If he could, the food would all be eaten by the people that need it. There are people that absolutely will take and eat this food because they are starving, but OP can’t deliver it to them.