Your estimates are based on what, grain production? That grain production equals meat and other things, not just produce. That estimate is also based on traditional row-cropping, is my guess.
Also, at the heart of it, your impression is incorrect. I didn't say the raised beds provided 50% of the family's calories, but 50% of our vegetable and other fresh produce needs. This does not include meat, most proteins in general, or fruits.
Finally, it is an assumption comparing traditional row cropping to square foot gardening in the raised beds. You get much more produce in a smaller space in square foot versus row crops, but it is much more labor intensive. You cannot use machinery in square foot gardens, compared to row crops. So there is a trade off.
In other words, the math doesn't work with your assumptions, because they're two different things. My estimate is that, while the garden produces 50% of our vegetable and produce needs, it's probably 10-20% of our overall caloric consumption. But that's a madey upey number, really. I have no idea.