Research data management has become an inevitable part of research, and both funding agencies and publishers nowadays require open and reusable data. This article focuses on one of the most prominent initiatives promoting reusability of research data - the FAIR guiding principles - nowadays widely accepted as the new standard for research data management. Through semi-structured interviews, we investigated researchers' experiences of practicing FAIR research data management within the context of a multi-stakeholder project within the field of health research funded by the European Commission. Our analysis showed that the informants' experiences of practicing FAIR research data management differed largely depending on which scientific tradition they belonged to; something that previous studies have attributed to shortcomings in the current infrastructure, lack of resources and persistent cultures around data sharing in the wider scientific community. Drawing on previous work presented within the field of Critical Data Studies (CDS), we argue that our findings point to a more fundamental problem; namely the failure to recognize that the FAIR framework is built on a positivist conceptualization of data. We argue that if FAIR is to have any chance of succeeding in its ambitions to be as inclusive and all-encompassing as it wants to be, these insights need to be taken more into account and provide some potential pathways.