I mean they didn't farm the whole acre, their garden plot was maybe 10 x 10 ft.

More than I can do in my town home, but not crazy.

Also economies of scale is a poor argument when it comes to farming. Prices on many crops is fixed by the Government. So yes they can produce food much cheaper, but they fix the price to be higher. If it wasn't for the government corn at our current rate of production would be nearly free, but it's artificially inflated.

I wanted to come back and address a few things in an edit. It seems like you're trying to imply they weren't poor and I'd like to address a few things. Firstly in the deep south, especially 50 years ago when they got the property, land was cheap and available. Many people owned some land and not much else. Hence the concept of "land rich" "cash poor". Plus selling your home is not a smart way to pay the bills. Secondly, they got the land after my great grandparents died the land was generational anyway. Thirdly, sure they had a house, but that didn't stop them from having to pick and choose between food and medicine. That didn't change the fact that my grandfather had no shoes for a period. I bought him a pair when I found out, but that's how he was. He'd rather do without than ask for help.

To adress the second part of your attempted "gotcha" yes having space to garden is a prerequisite to gardening, then uh yeah it is. The other option is leasing some land for a small garden, and yeah of course that's going to be expensive