Yodsanklai is referring to the mythical food deserts.

We study the causes of “nutritional inequality”: why the wealthy tend to eat more healthfully than the poor in the U.S. Using two event study designs exploiting entry of new supermarkets and households’ moves to healthier neighborhoods, we reject that neighborhood environments have economically meaningful effects on healthy eating. Using a structural demand model, we find that exposing low-income households to the same food availability and prices experienced by high-income households would reduce nutritional inequality by only 9%, while the remaining 91% is driven by differences in demand. In turn, these income-related demand differences are partially explained by education, nutrition knowledge, and regional preferences. These findings contrast with discussions of nutritional inequality that emphasize supply-side issues such as food deserts.

https://web.stanford.edu/~diamondr/AllcottDiamondDube_FoodDe...

The term 'Food desert' was used primarily to refer to total healthy food availability within a certain radius, including (especially) healthy food availability in supermarkets.

Yodsanklai appears to have been referring to the availability of healthy prepared foods, particularly restaurant foods. It is entirely possible to live in an area well-served with supermarkets and bodegas and only have 'unhealthy' restaurants to choose from due to the peculiar demands of that area. You can drive through parts of the US and see nothing but greasy spoons or pub food, while the local at-home cooks have access to a wider variety of healthy foods from the markets.

> we find that exposing low-income households to the same food availability and prices experienced by high-income household

Not sure how the researchers at Stanford couldn’t conclude that poor people aren’t going to pay rich people prices

The following is the remainder of the sentence you quoted

> would reduce nutritional inequality by only 9%, while the remaining 91% is driven by differences in demand.

Most of the difference in what the underclass and others eat is because of taste. And Americans spend less of their budgets on food consumed at home than any other nation.

https://ourworldindata.org/food-prices/#consumer-expenditure...

And healthy food is at worst only very slightly cheaper than unhealthy food

http://bmjopen.bmj.com/content/3/12/e004277.full?sid=820d6e1...

i saw the rest of the sentence. You still appear to be glossing over the point, which the rest of that sentence does not refute.

The sodium and oil quantities disqualify most places automatically.

It's also more expensive to provide healthy, fresh food and restaurants being famously low margin businesses can't afford to give this to you unless you're in a wealthy area with others who are willing to spend for it.

I did several road trips (mainly in the West) in the US and I clearly remember that I would go for days only eating junk food. It was difficult to find anything else.