India and other economies in the Global South are undergoing a proliferation in public Wi-Fi, with large-scale deployments from industry and government. In this paper, we report on a qualitative study on public Wi-Fi conceptions as held by urban Indians, a priori to connecting to a network. Our findings show that prior public Wi-Fi users and non-users alike raised a surprising range and depth of conceptions---ranging from suspicion of operators' intentions to monetize, to concerns about sexual image morphing, to fears of phone wipeouts, to aspiration---which were informed by popular media, BlueTooth cultures, and social learning. We found these conceptions of Wi-Fi networks to significantly influence adoption of public Wi-Fi. With enormous investments in public Wi-Fi initiatives, we call for network providers to address these deep conceptions among emerging users; by suggesting ways to build public awareness, better user experiences, and business model innovation.