That's kind of the point though. Without a blockchain, who would ultimately be responsible for the centralized database? Barcodes keep track of a particular product from a particular company but that company may source the product (lettuce in this case) from numerous farms. Things like barcodes don't generally keep track of things on that level. Plus, a particular farm and/or distributor may have incentive to lie which they couldn't do in a blockchain environment. It's not that this couldn't be done without a blockchain but then you would have to set up some central authority for running such a database, keeping track of everything, and ensuring the data is correct. I'm not sure who such an authority would be.

From the story:

That’s why Walmart and other grocers have already put this technology to test—with much success. When Walmart tested the technology with the recall of a batch of mangos, the time it took to trace the produce back to its farm was reduced from seven days to just 2.2 seconds.