This paper captures the results of our research in 2019 into Children's data privacy. It explores how parents and teenagers conceptualise corporations and their surveillance of their internet activities. It provides a fresh approach to studies around online privacy which had to date been focused on teenagers' practices within social media sites, by examining how parents and teenagers understand and conceptualise privacy in the digital context. This paper challenges existing neoliberal policy frameworks that presume educators and parents, and even teenagers themselves, will through education develop the motivation to protect children's data privacy. This research found that their notions of privacy risk and harm remain embedded within the social rather than technological contexts, prohibiting concerns about corporate surveillance.