There's not much need for skepticism here. Pay even the tiniest amount of attention to prices at the supermarket, and you'll know that it's true. I can buy a can of beef stew for $5. Buying the raw ingredients to make the same quantity of beef stew would cost me at least $10.
Make friends with your freezer. Meat production, like everything else, goes in cycles so at regular intervals producers (and thus) supermarkets will find themselves with excess stock of this or that. The obvious example is buying turkey after Thanksgiving, but I see cycles in things like the price of pork every 4-6 weeks. So about every other month I buy a whole boneless pork loin (a single piece of meat about as long as your forearm) for about $25 instead of the usual cost of around $50. I spend about 20 minutes at home slicing it into pork steaks and freezing most of them, and get 20+ nice thick steaks out of it, so that's about $1.05 each. Add in the cost of the vegetables, other ingredients, energy to cool and cook, and the price of a good size meal is still only $2.50 at most.
That's a particularly good deal (which is why I buy it so regularly) but if you can cook and don't mind forward planning your food a bit, you save a lot of money. Menu planning probably cuts your cost by 50% vs. buying your ingredients on a per-meal basis.
And this isn't surprising: $5 is remarkably cheap for a beef-based product. They do it by using remnant beef, which you can't really get in stores. Grocery store stew meat is probably 2-3x more expensive than the stuff they're using. Mine will taste better and be higher quality, but it won't be cheaper.
I can't understand how you come to this conclusion. I definitely save money by buying larger cuts or bulk packs. Maybe you should come over for dinner :-)