And yet, the very study you linked to concluded that despite 5 years of research on the topic, it still isn't clear what the actual causes are. But you know, I definitely think your arm-chair reasoning probably contains the one true reason.

Research has mostly focused on explaining the paradox at a household level. Farrell and colleagues reviewed the literature pertaining to low- and middle-income countries and focused on the bigger picture, that is, analyzing the issue at an individual, household, community, and country level. They proposed 5 context-mechanisms factors that could modify the association between an individual’s food insecurity and obesity risk: affordability of energy dense, processed foods, quantity & diversity of food consumed, spatial temporal access to nutritious food, interpersonal distribution of food and non- dietary behavior. Nevertheless, affordability of energy dense foods was identified as the main mechanism since the authors had limited evidence to support the other mechanisms (26). Other authors have proposed that social support can also play a role since they found that food insecure women who reported lower levels of social support were more likely to be obese (28)