I've released many federal documents in my time in which I removed Personally Identifiable Information. I don't see why the same can't be done here. Click on the Excel columns with the store name and exact address (keep the county) and hit delete, then disseminate the report.
The story was lacking in info, but it appeared to me the data requestors were more interested in how much money was going to admin costs, how much was going to food, and how much of that food might have been filet mignon, Fritos, etc. If they were interested in where it was being spent, for the purposes of the report it seems county level data would have been acceptable.
All that said, the closest store to my folks' place is a Food Max. My dad always complains because 90% of the time, he's the only guy in line actually paying for his food. That's not the case at another store a few miles further away, though both take the old EBT. So maybe people who use food stamps prefer certain stores, or certain stores are friendlier, or give deals to, people with food stamps.
If it's public (i.e., MY money), and it's being used on luxury food or junk food, I have a right to know, and it seems an establishment accepting public money has an obligation to provide the information. Obviously this wouldn't be the case with something like hospitals and medical records, but I can't find any reason to make food purchases using public funds private. If you don't want people to know what you buy at the grocery store, do what I do: Give a fake name and number for your "rewards card" and pay cash at the self checkout. My Ding Dongs are my business, but then I pay for them with my own money.