Using novel data describing the healthfulness of household food purchases and the retail landscapes consumers face, we measure the role of access in explaining why wealthier and more educated households purchase healthier foods. We find that spatial differences in access, though significant, are small relative to spatial differences in the nutritional content of sales. Socioeconomic disparities in nutritional consumption exist even among households with equivalent access, and the healthfulness of household consumption responds minimally to improvements in local retain environments. Our results indicate that access-improving policies alone will eliminate less than one third of existing socioeconomic disparities in nutritional consumption.