It's a bit counterintuitive but is probably kind of correct.
Low income does not per se mean lower quality diet in the US. In fact, a healthy diet based on high quality food can be less expensive than a less health lower quality food based diet.
However sources of high quality inexpensive foods are not evenly distributed. Many a low income neighborhood does not have a grocery store that caries such things. Many only have convenience stores like 7-11. Often those neighborhoods also don't have good and affordable public transit making it had for many residents to get to a real grocery store.
And so there will be a tendency for lower income to result in a lower quality diet.
These places where people have food access limits inside of countries that mostly have pretty good distribution are called "food deserts", and they are not just in the US [1].
[1] https://en.wikipedia.org/wiki/Food_deserts_by_country