I think that part of the findings is key. If car ownership is limited in poor neighborhoods, then "a couple of miles" is not always easily accessible. Good public transit routes can help with that. Bikes and walking are a bigger challenge for groceries over the span of a couple miles.
It sounds like these findings consider the distance the same regardless of transportation method. I'd compare 2 miles to get groceries on foot to 50 miles to get groceries in a car.
That's a good point. Schlepping groceries via bike or walking is a total PITA.
From the article, though:
She used census tracts to define neighborhoods because they tend to have economically homogeneous populations. Poor neighborhoods, Dr. Lee found, had nearly twice as many fast food restaurants and convenience stores as wealthier ones, and they had more than three times as many corner stores per square mile. But they also had nearly twice as many supermarkets and large-scale grocers per square mile. Her study, financed by the institute, was published in the March issue of Social Science and Medicine.
Dr. Sturm’s study, published in February in The American Journal of Preventive Medicine, had a different design. With financing from the National Institutes of Health, he used data on the self-reported heights, weights, and diets of more than 13,000 California children and teenagers in the California Health Interview Survey. The survey included the students’ addresses and the addresses of their schools. He used a different data set to see what food outlets were nearby. Dr. Sturm found no relationship between what type of food students said they ate, what they weighed, and the type of food within a mile and a half of their homes.
Sturm's study would seem to cover those without access to a car and Lee's study seems to show the effects of density ( more stores of all types available in a given area ).