If you find someone with access to Nielsen sales data, it's enlightening. Walmart is very rarely the cheapest retailer. It's been a few years, but I believe the rock bottom, cheapest grocer was Aldi, by a huge margin.
That wouldn't surprise me since they are selling almost entirely store brand / generic items. When I first got out of college, I largely shopped at Aldi's and it was certainly the cheapest way to buy food. I ultimately stopped because they sold very little fresh food. I think they're starting to sell a lot more now but I'm not sure how those prices compare.