Sure, but I'm not inclined to believe that number on its own. Practically, even the cheapest grocer like Aldi could turn out to be expensive than the quoted $3.37.
Rice and beans - been my staple for most of my life - isn't too much more than this. Two cup dried rice + two can beans is around $4 and that is generally enough for me. Although it is much better with a few eggs and some hot sauce or salsa as well.
The CPI is, for largely good reasons, primarily tracking things other than groceries, so it's arguably indeed pretty useless in comparing these over time.