Is there a citation for this? TBH it sounds like a just so story - in my experience, grocery store prices in a city are pretty uniform.
One of the biggest cognitive fallacies of the human brain is thinking that you can accurately aggregate and compare prices in this manner. Its one of the reasons that airplane tickets are sold the way they are.
They just also gave their impression. They didn't imply that it was a comprehensive study or scientific.
And they're right to ask. They shouldn't believe something just because someone said it on the internet.
In addition, there's usually some "nicer" grocery stores where you pay a premium to never have to wait in line behind someone using EBT though I think Whole Foods mostly dominates that niche these days.
And then there's availability: some veggies are not readily available outside of asian grocery stores and meat prices can vary widely from store to store.
Good lord, ours aren't. Our most-convenient grocery store has prices like 25% higher than Wal-Mart, ~15% higher than a couple larger grocery stores farther away, and 10% higher than Target.