In response to a recent commentary (Tigard, in press) on my previous article, 'The Collective Nature of Personalized Medicine' (McGonigle, 2016), herein I discuss collective responsibilities and rights in relation to the ethics of genomic data and personalized medicine. I respond to and elaborate on some of the issues Tigard raises and I draw on the anthropological concept of 'dividuality' to emphasize the precisely shared nature of genomic data in order to illuminate the ethical complexity surrounding their protection. Overall, I argue that genomic data, by virtue of their distributed and shared nature, necessitate novel approaches for bioethical assessment.