Food deserts, places where residents lack nearby supermarkets, have received attention from the media, academics, policy-makers, and activists. The popular policy response is to establish a new supermarket. Yet, communities who live in food deserts may already have their own well-adapted strategies to access healthy food. In this article, we argue that policy-makers all too often overlook in situ opportunities, and may even disrupt low-cost healthy food access options with supermarket interventions. We use evidence to make two main points. First, we demonstrate the limitations of focusing on food deserts when interpreting diet-related health disparities. By conducting a US national county-level multi-variable spatial regression analysis of socio-economic status, built environment and food environment factors, we determine that diet-related health outcomes do not clearly correlate with supermarket access. Instead, health outcomes are most strongly associated with income and race. This suggests that interventions to improve healthy eating should begin with a focus on anti-poverty. Second, we identify alternative paths, beyond supermarkets, to healthy food access through a literature review.