Yea, but there's one problem I have with this estimate. It requires near perfect efficiency. There's almost no buffer here for poor crop yields, less than ideal climate conditions, weeds overtaking, pest destruction, wrong breed of crop for conditions, soil/hydroponic management, etc. For 500 sq ft to be viable for 4 people, it needs to be taken care of in a very regiment fashion.
Not saying it's impossible. But that number shouldn't be advised for beginner homesteaders or people with less than ideal time to spend on the garden. It's great if at least one person out of four can devote a good amount of their time everyday to it and are already well experienced (hands on experience, not just internet articles) in horticulture.
Plus, you generally want plenty extra to harvest so you can jar, can, preserve however you want. That way in case you do happen to have a bad next yield, you still have something. Don't forget about seed-saving too. Most plants you have to sacrifice from eating to some capacity so you can plant again next season. Let's not forget the compost pile too to help re-fertilize soil and some rest time for the soil if you can't properly maintain it.
Oh and back on climate. Here in Florida, yea, I could probably figure it out with 500 sq ft. I have like a 10 month growing season here. Easy. Throw up a greenhouse with a heater that only needs to be ran maybe 10 days out of the year, at most, then I have 12 months. I can compost small piles fast all year round. It's near perfect here. Michigan? Ha! I know there are certain types of greenhouse designs that extend the growing seasons in places like Alaska to a certain extent and somewhat efficiently. But that's a lot more effort and work that most people aren't willing to do.
Long way of me just saying, that 500 sq ft for 4 people year round needs a heavy asterisk of "Under ideal and perfect conditions".
But my rant also requires an asterisk. I'm not saying that if you can't grow all your food, then don't grow anything. I think everyone should grow at least some of their own food in a manner that fits their wants, conditions and lifestyle. Just... have realistic expectations. I hate to see people have unrealistic expectations with gardening and be disappointed. Misses the point to the whole venture. There are downsides too. As a kid we grew our own tomatoes for fun. Nothing serious or wide scale. Like 10 plants a year. Problem with that (besides caterpillars), I absolutely hate most store bought tomatoes, even 20 years later. I have to have organic farmer's market grown or my own. Anything conventional store bought is just red-dyed, solidified water.